Answer:
Step-by-step explanation:
Let us assume that we have n different dots on a paper. We are to connect pairwise by a line. We have to find out how many lines can be formed.
Let us prove by induction.
If there is one dot then we have no line = 1(1-1) =0
Thus n(n-1) is true for 1 dot
Let us assume that for n dots we have n(n-1) lines
Add one more point now total points are n+1.
Already the existing n points are connected by a line.
So the extra point has to be connected to each of n point
i.e. n lines should be added from the new point to the n points and again n lines from the points to the new point(Assuming lines are different if initial and final point are different)
So 2n lines would be added
So total number of lines for n+1 points
[tex]= n(n-1) +n+n= n^2-n+2n \\= n^2+n\\=n(n+1)[/tex]
Thus true for n+1 if true for n. Already true for n =1
So proved by induction for all natural numbers n.
Using mathematical induction, we prove the number of lines connecting pairs of dots for n dots is n(n-1)/2. We confirm the base case for n=1 and then assume the proposition holds for k, leading to it holding for k+1, thus proving it for all natural numbers n.
The question involves calculating the number of lines that can be drawn to connect each pair of dots on a paper. To find this number for n dots, we can use mathematical induction.
Let's denote P(n) as the proposition that for n dots, the number of lines required to connect each pair of dots is n(n-1)/2, which simplifies to the sum of the first n-1 natural numbers.
Base Case
For n=1, there are no lines needed since there is only one dot, and no connections to be made: P(1) holds because 1(1-1)/2 = 0.
Inductive Step
We assume that P(k) is true for some natural number k, meaning that k dots require k(k-1)/2 lines. Now, we consider n=k+1 dots. The new dot must be connected to each of the k existing dots, adding k new lines. Therefore, the total number of lines for k+1 dots is k(k-1)/2 + k, which simplifies to (k+1)k/2, and is exactly P(k+1).
By the principle of mathematical induction, since we have proven the base case and the inductive step, we conclude that P(n) holds for all natural numbers n.
X minus 12 is 30 what’s the answer
Answer:
x=42
Step-by-step explanation:
x-12=30
x=30+12
x=42
To solve for x in this equation, we want to get x by itself on the left side of the equation. Since 12 is being subtracted from x, to get x by itself, we need to add 12 to the left side of the equation. If we add 12 to the left side, we must also add 12 to the right side.
On the left side, -12 and +12 cancel each other out so we are simply left with x. On the right side, 30 + 12 is 42 so we have x = 42.
It's important to understand that we can check our answer by substituting 42 back into the original equation.
So we have (42) - 12 = 30.
42 - 12 is 30 so we have 30 = 30 which is a true statement so our answer, x = 42, is correct.
The point P(21,35) is on the terminal side of an angle in standard position. What is the distance from P to the origin?
Answer:
The distance from P to origin is approximately 40.82 units.
Step-by-step explanation:
We are given the following in the data:
The point P(21,35)
We have to find the distance of point P from the origin.
Coordinates of origin: (0,0)
Distance formula:
[tex](x_1,y_1),(x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
Putting the values, we get,
[tex](21,35), (0,0)\\\\d = \sqrt{(0-21)^2 + (0-35)^2} = \sqrt{1666} = 7\sqrt{34} \approx 40.82\text{ units}[/tex]
The distance from P to origin is approximately 40.82 units.
!!!!URGENT!!!!
Find the first 3 Iterations of the function here: g(x)=1/3x+1 if you have an initial value of 2.
An example on how to complete it below.
Answer:
1st it: g(2)=1/3(2)+1=0.67+1=1.67
2nd it: g^2(2)=1/3(1.67)+1=0.56+1=1.56
3rd it: g^3(2)=1/3(1.56)+1=0.52+1=1.52
Answer:
The first three iterations are 1.67, 1.56 and 1.52
Step-by-step explanation:
Given the function g(x)=1/3x+1
To get the first threw iteration with initial value of x = 2
First iteration at x= 2:
g(2) = 2/3+1
g(2) = (2+3)/3
g(2) = 5/3 = 1.67
Second iteration will be when x = g(2) = 5/3
g²(2) = g(5/3) = 1/3(5/3) + 1
g²(2) = g(5/3) = 5/9 + 1
g²(2) = g(5/3) = 14/9 = 1.56
Third iteration will be at when
x = g²(2) = 14/9
g³(2) = g(14/9) = 1/3(14/9) + 1
g³(2) = g(14/9) = 14/27 + 1
g³(2) = g(14/9) = 41/27 = 1.52
The first three iterations are 1.67, 1.56 and 1.52
having trouble with this and 3 others (part 3)
Answer:
a.) 23
b.) y=14
c.) 23
d.) -23
e.) T=8
f.) f=1/8
Step-by-step explanation:
a.) general equation is Asin((2π/T))
A is the amplitude. It's A value is 23
b.) Midline = vertical_shift = 14
c.) max = positive amplitude value = 23
d.) min = negative amplitude = -23
e.) Factor out 2π from your angular frequency to get the period.
ω = π/4 = (2π)/8 = (2π)/T
Period = 8
f.) Frequency is just the inverse of the period.
f = 1/T = 1/8
A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular Norman window is to be 24 feet. What should the rectangle's dimensions be in order to maximize the area of the window and, therefore, allow in as much light as possible?
To maximize the area of the Norman window, solve for the dimensions of the rectangle. Substitute the expression for 'h' in terms of 'w' into the area formula. Take the derivative of A with respect to 'w', set it equal to zero, and solve for 'w'.
Explanation:To maximize the area of the Norman window, we need to find the dimensions of the rectangle. Let's denote the width of the rectangle as 'w' and the height as 'h'. The perimeter of the rectangle can be expressed as 2w + h + πh = 24 feet. Rearranging the equation, we have (2 + π)h + 2w = 24. Since we want to maximize the area, we can solve for 'h' in terms of 'w' using this equation.
Next, we can substitute the expression for 'h' in terms of 'w' into the area formula for the window, which is A = wh + (π/4)w^2. Simplifying this expression, we get A = (w(2 + πw))/4. To find the dimensions that maximize the area, we can take the derivative of A with respect to 'w', set it equal to zero, and solve for 'w'. This will give us the width of the rectangle. Once we have the width, we can substitute it back into the equation for 'h' to find the height.
By solving these equations, we can find the dimensions of the rectangle that will maximize the area of the Norman window, allowing in as much light as possible.
a. Is the statement "Every elementary row operation is reversible" true or false? Explain. A. True, because interchanging can be reversed by scaling, and scaling can be reversed by replacement. B. False, because only scaling and interchanging are reversible row operations. C. True, because replacement, interchanging, and scaling are all reversible. D. False, because only interchanging is a reversible row operation.
The statement "Every elementary row operation is reversible" is true because interchanging can be reversed by scaling, and scaling can be reversed by replacement (Option A is correct).
The statement "Every elementary row operation is reversible" is true.
The correct choice is: A. True, because interchanging can be reversed by scaling, and scaling can be reversed by replacement.
- Interchanging rows (row swapping) can be reversed by another interchange.
- Scaling a row by a non-zero scalar can be reversed by scaling it by the reciprocal of that scalar.
- Replacement operations (adding or subtracting multiples of one row from another) can also be reversed by adding or subtracting the same multiples in the opposite direction.
So, all three elementary row operations (replacement, interchanging, and scaling) are reversible, which makes option A the correct choice.
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The statement 'Every elementary row operation is reversible' is true. All the three types of elementary row operations, i.e., scaling, interchanging, and replacement, can be reversed using appropriate methods.
Explanation:The statement 'Every elementary row operation is reversible' is indeed true. The three types of elementary row operations, i.e., scaling, interchanging, and replacement, are all reversible. Scaling can be reversed by multiplying the row by the reciprocal of the scale factor. Interchanging rows can be undone by simply interchanging them again. Replacement can be reversed by applying a replacement operation with the opposite sign.
For example, if you multiply a row by a factor of 3 (scaling), you can reverse this by multiplying the row by 1/3. If you interchange row 1 and row 2, you can reverse this by interchanging these two rows again. Finally, if you replaced row 1 by adding 2*row 2 to it, you could reverse this by replacing row 1 by subtracting the same 2*row 2 from it.
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A garden supply store sells two types of lawn mowers. Total ales of mowers for the year were $8379.70. The total number of mowers sold the 30. The small mower cost $249.99 and the large mower costs $329.99.
Write and solve a system of equations to find the number sold of each type of mower.
Answer:
The number of small mowers are 19 and the large mowers are 11.
Step-by-step explanation:
Given:
A garden supply store sells two types of lawn mowers. Total sales of mowers for the year were $8379.70. The total number of mowers sold the 30. The small mower cost $249.99 and the large mower costs $329.99.
Now, to find the number of each type of mower sold.
Let the number of small mower be [tex]x.[/tex]
And the number of large mower be [tex]y.[/tex]
So, total number of mowers are:
[tex]x+y=30[/tex]
[tex]x=30-y\ \ \ ....(1)[/tex]
Now, the total sales of mowers are:
[tex]249.99(x)+329.99(y)=8379.70[/tex]
Substituting the value of [tex]x[/tex] from equation (1) we get:
[tex]249.99(30-y)+329.99y=8379.70[/tex]
[tex]7499.7-249.99y+329.99y=8379.70[/tex]
[tex]7499.7+80y=8379.70[/tex]
Subtracting both sides by 7499.7 we get:
[tex]80y=880[/tex]
Dividing both sides by 80 we get:
[tex]y=11.[/tex]
The number of large mower = 11.
Now, to get the number of small mowers we substitute the value of [tex]y[/tex] in equation ( 1 ):
[tex]x=30-y\\x=30-11\\x=19.[/tex]
The number of small mower = 19.
Therefore, the number of small mowers are 19 and the large mowers are 11.
The sketch shows the floor plan of a bathroom. The shower tray is 2'6" square and is
fixed to the floor. The toilet and washbasin are both wall mounted.
14) Allowing for 15% wastage, approximately how many square yards of floor tiles should
be ordered?
A
7.25
B
6.25
C
9.25
D
5.50
E
8.50
Write a formula that describes the value of an initial investment of $1,200, growing an interest rate of 4% compounded continuously.
Continuous compound is e^rate x time
The formula would be D. 1200e^0.04t
Answer: OPTION D A = 1200.e(0.04)(t)
Step-by-step explanation:
If the interest is compounded continuously for t years at a rate of r per year, then the compounded amount is given by:
A = P. e rt
P =$1200, r = 4% , t = t years
A = 1200.e(0.04)(t)
A graduated cylinder with 10.0 mL of water ha mass of 25.0 g. 51 paper clips are added to the graduated cylinder . The total mass is 28 and the total volume is 14.7. What is the density of the paper clips? (Calculate your answer to 2 decimal places)
Answer: The density of the paper clips is 0.64 g/ml.
Step-by-step explanation:
Given : Volume of water = 10.0 mL
mass of water = 25.0 g
After 51 clips added to water , the total mass = 28 g
Total volume = 14.7
Mass of clips = total mass - mass of water
= 28 g-25g = 3g
Volume of clips = Total volume- Volume of water
= 14.7- 10.0 = 4.7 ml
Density of paper clips =[tex]\dfrac{\text{Mass of paper clips}}{\text{Volume of paper clips}}[/tex]
[tex]=\dfrac{3}{4.7}=0.638297\approx0.64\ g/ml[/tex]
Hence, the density of the paper clips is 0.64 g/ml.
Answer:
The density of the paper clips is 0.64 g/m
Step-by-step explanation:
hope this helps :)
A three-phase lesson format provides a structure for students to have inquiry on a topic, engage in the content through action and discussion and time to reflect and make connections. What statement below demonstrates the Before related agendas?
A) Be sure the task is understood.
B) Let go
C) Provide extensions.
D) Identify future problems.
Answer:
A) Be sure the task is understood.
Step-by-step explanation:
The principle "Make sure the mission is understood, performed, and achieved."
Another way we talk about this principle in the Navy is through the idea of "intrusive leadership." In some respects both "micromanagement" and "intrusive leadership" sound terrible.
Think about certain great managers and leaders you have had in your career yet again. Probability are they will be the ones who asked you those difficult questions, too.
They moved everyone to new technical levels, and eye for detail. When you said you knew what you were doing or when you announced the progress of a project, they didn't necessarily take it to face value.
A Cepheid variable star is a star whose brightness alternately increases and decreases. Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 6.6 days. Its average brightness is 2.6 and the brightness changes by /-0.6. Using this data, we can construct a mathematical model for the brightness of Cephei Joe at time t, where t is measured in days:
(a) Find the rate of change of the brightness after t days.
(b) Find the rate of increase after one day.
Answer:
a) Rate of brightness after t days = B(t) = 2.6 + 0.6sin(2×3.142 t /6.6)
b) 0.57
Step-by-step explanation:
Given
Number of days=6,6 days
Average brightness =2.6
B(t)= 2.6 + 0.6 sin (2× 3.142t/6.6)
b) B(1day) = 0.6 ×(2×3.142/6.6)cos (2×3.142/6.6)
B(1 day) = 0.6 × (6.248/6.6)cos 0.952
B(1 day) =0.6 × 0.952 ×0.9999
B(1day) = 0.5711
= 0.57
If the probability is 0.54 that Stock A will increase in value during the next month and the probability is 0.68 that Stock B will increase in value during the next month, what is the greatest possible value for the probability that neither of these two events will occur.
P(A) =0.54
P(B)= 0.68
P'(A)= 1-0.54 = 0.46
P'(B)= 1- 0.68 = 0.32
The probability of neither of both event will occur:
= P'(A)×P'(B)
=0.46 × 0.32
=0.1472
x-6y +4z=-12
x+y-4z=12
2x + 2y + 5z =-15
Systems of equations with three variables and three equations
Answer:
x = 0 , y = 0 , z = -3
Step-by-step explanation:
Solve the following system:
{x - 6 y + 4 z = -12 | (equation 1)
x + y - 4 z = 12 | (equation 2)
2 x + 2 y + 5 z = -15 | (equation 3)
Swap equation 1 with equation 3:
{2 x + 2 y + 5 z = -15 | (equation 1)
x + y - 4 z = 12 | (equation 2)
x - 6 y + 4 z = -12 | (equation 3)
Subtract 1/2 × (equation 1) from equation 2:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - (13 z)/2 = 39/2 | (equation 2)
x - 6 y + 4 z = -12 | (equation 3)
Multiply equation 2 by 2/13:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - z = 3 | (equation 2)
x - 6 y + 4 z = -12 | (equation 3)
Subtract 1/2 × (equation 1) from equation 3:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - z = 3 | (equation 2)
0 x - 7 y + (3 z)/2 = -9/2 | (equation 3)
Multiply equation 3 by 2:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - z = 3 | (equation 2)
0 x - 14 y + 3 z = -9 | (equation 3)
Swap equation 2 with equation 3:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x - 14 y + 3 z = -9 | (equation 2)
0 x+0 y - z = 3 | (equation 3)
Multiply equation 3 by -1:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x - 14 y + 3 z = -9 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 3 × (equation 3) from equation 2:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x - 14 y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Divide equation 2 by -14:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 2 × (equation 2) from equation 1:
{2 x + 0 y+5 z = -15 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 5 × (equation 3) from equation 1:
{2 x+0 y+0 z = 0 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Divide equation 1 by 2:
{x+0 y+0 z = 0 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Collect results:
Answer: {x = 0 , y = 0 , z = -3
To solve the given system of equations, use the method of elimination to eliminate one variable at a time and solve for the remaining variables.
Explanation:To solve the system of equations:
x - 6y + 4z = -12
x + y - 4z = 12
2x + 2y + 5z = -15
We can use the method of substitution or elimination. Let's use the method of elimination:
Multiply the second equation by 2:Multiply the third equation by 3:Add the new second and third equations to the first equation:Solve the resulting equation:Therefore, the solution is x = -5, y = 4, and z = 1.
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The hourly operating cost of a certain plane, which seats up to 295 passengers, is estimated to be $3,945. If an airline charges passenger a fare of $95 per hour of flight, find the hourly profit P it earns operating the plane as a function of the number of passengers x. P(x) = Specify the domain. 0 lessthanorequalto x lessthanorequalto infinity 0 lessthanorequalto x lessthanorequalto 295 0 < x < 295 295 lessthanorequalto x lessthanorequalto infinity What is the least number of passengers it must carry to make a profit? The Metropolitan Company sells its latest product at a unit price of $3. Variable costs are estimated to be 50% of the total revenue, while fixed costs amount to $6,600 per month. How many units should the company sell per month to break even, assuming that it can sell up to 5,000 units per month at the planned price? units
Answer:
42 passengers 4400 unitsStep-by-step explanation:
Please refer to the picture below
A test of intelligence is given to a subject. The subject scores 110 on the first administration. Six months later, the same subject is given the same test again and receives a score of 75. After another six months has passed, the subject is given the test one last time and receives a score of 138. What conclusions can be drawn from these scores?The scores are not valid.
Answer:
True, the scores are not valid.
Step-by-step explanation:
The test supposed to be measuring intelligence. We can assume that the intelligence of most people relatively stable (will not change too much over a short amount of time), and can expect it should go upward with brain growth and education. But the test seems to give a huge decrease from the first and second results. Then the third result is a huge increase that even higher than the first test.
We don't know the true value of the subject, but seeing the huge gap for every repetition we can tell that the test result lacks precision.
HELP ASAP!!! will give brainliest to best answer!!
What proportional segment lengths verify that XZ¯¯¯¯¯∥PQ¯¯¯¯¯ ?
Fill in the boxes to correctly complete the proportion.
Answer:
[tex]\frac{16}{21}=\frac{8}{10.5}[/tex]
or
[tex]\frac{16}{8}=\frac{21}{10.5}[/tex]
Step-by-step explanation:
we know that
If two figures are similar then the ratio of its corresponding sides is proportional
In this problem
triangle YPQ and triangle YXZ are similar by AA Similarity Theorem
so
[tex]\frac{YP}{YX}=\frac{YQ}{YZ}[/tex]
substitute the given values
[tex]\frac{16}{21}=\frac{8}{10.5}[/tex]
Rewrite
[tex]\frac{16}{8}=\frac{21}{10.5}[/tex]
The boxes should be filled with [tex]\frac{16}{21} = \frac{8}{10.5}\\\\\frac{16}{8} = \frac{21}{10.5}[/tex]
The calculation is as follows:As we know that
In the case when two figures are similar so the ratio of its corresponding sides is proportional
In this given situation
triangle YPQ and triangle YXZ are similar by AA Similarity Theorem
So,
[tex]\frac{YP}{YX} = \frac{YQ}{YZ}[/tex]
[tex]\frac{16}{21} = \frac{8}{10.5}\\\\\frac{16}{8} = \frac{21}{10.5}[/tex]
It can be any of the both.
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Study Island: Gina has 24 more barrettes than Holly. The equation g = 24 + h, where g represents the number of barrettes Gina has, and h represents the number of barrettes Holly has, shows this relationship. If Gina has 51 barrettes, how many barrettes does Holly have?
See picture for solution and answer.
From January to June, a company spent $60 per month on office supplies. In July the price of office supplies increased by 15% and remained the same for the rest of the year. How much did the company spend an office supplies for the year
Answer:
$774
Step-by-step explanation:
We have been given that from January to June, a company spent $60 per month on office supplies. In July the price of office supplies increased by 15% and remained the same for the rest of the year.
Let us find increased cost of supplies as shown below:
[tex]\text{Increased cost of supplies}=60+\frac{15}{100}\times 60[/tex]
[tex]\text{Increased cost of supplies}=60+0.15\times 60[/tex]
[tex]\text{Increased cost of supplies}=60+9[/tex]
[tex]\text{Increased cost of supplies}=69[/tex]
There are 6 months from January to June, so cost of supplies on these 6 months would be 6 times $60.
There are 6 months from July to December, so cost of these months would be 6 times $69.
Total cost will be equal to sum of these two amounts.
[tex]\text{Amount spent on office supply in the year}=6\times \$60+6\times \$69[/tex]
[tex]\text{Amount spent on office supply in the year}=6( \$60+\$69)[/tex]
[tex]\text{Amount spent on office supply in the year}=6( \$129)[/tex]
[tex]\text{Amount spent on office supply in the year}=\$774[/tex]
Therefore, $774 were spent on office supplies.
Melody has hired a new accountant. He has gathered her pay stubs and is trying to determine how many CDs were sold during each month of the previous year. Her pay stub for June indicates that she made $4,889 in that month. Write an equation her accountant could use to determine how many CDs were sold in June
Answer:
The required equation is [tex]4889=4850 +3n[/tex].
Step-by-step explanation:
Consider the provided information.
Melody has a new job recording for the All-Time Favorites record label.
She is paid a monthly base salary of $plus $3 for each CD sold.
Her pay stub for June indicates that she made $4,889 in that month.
Let n represents the number of CDs she sold.
Therefore, the required equation is [tex]4889=4850 +3n[/tex].
1.
A 0.40 kg football is thrown with a velocity of 15 m/s to the right. A stationary receiver
catches the ball and brings it to rest in 0.20 s. What is the force exerted on the ball by
the receiver?
Yo sup??
From Newton's 2nd law of motion
F*t=Δp
=mv-mu
mu=0.4*15
=6
t=0.2
mv=0
Therefore
F*0.2=6
F=30 N
Hope this helps.
What is the pressure difference Δp=pinside−poutside? Use 1.28 kg/m3 for the density of air. Treat the air as an ideal fluid obeying Bernoulli's equation.
This is an incomplete question, here is a complete question.
A hurricane wind blows across a 7.00 m × 12.0 m flat roof at a speed of 150 km/h.
What is the pressure difference Δp = p(inside)-p(outside)? Use 1.28 kg/m³ for the density of air. Treat the air as an ideal fluid obeying Bernoulli's equation.
Answer : The pressure difference will be, [tex]1.11\times 10^3Pa[/tex]
Step-by-step explanation :
As we are given:
Speed = 150 km/h = 41.66 m/s
Density = [tex]\rho=1.28kg/m^3[/tex]
Area = A = 7.00 m × 12.0 m
Formula used :
[tex]\Delta P=\frac{1}{2}\times \rho \times v^2[/tex]
Now put all the given values in this formula, we get:
[tex]\Delta P=\frac{1}{2}\times (1.28kg/m^3)\times (41.66m/s)^2[/tex]
[tex]\Delta P=1.11\times 10^3Pa[/tex]
Thus, the pressure difference will be, [tex]1.11\times 10^3Pa[/tex]
A pizza chain was willing to pay $1 to each person interviewed about his or her likes and dis- likes of types of pizza crust. Of the people interviewed, 200 liked thin crust, 270 liked thick crust, 70 liked both, and 50 did not like either type of crust. What was the total cost of the survey?
Answer:
Total cost of the survey = $450
Step-by-step explanation:
Given:
Cost for each person = $1
Liked thin crust = 200 people
Liked thick crust = 270 people
Both crust like = 70 people
50 people did not like either type of crust.
We need to find the total cost of the survey.
Solution:
Number of people who like thin crust or thick crust.
⇒ 200 + 270 - 70
⇒ 470 - 70
⇒ 400
So, 400 people likes thin crust OR thick crust.
And, also 50 peoples did not likes either thin crust OR thick crust.
So, we add 50 people who did not like any type of pizza.
⇒ 400 + 50
Therefore, total cost of the survey = $450
The nieces is it a ladder to clean the outside of her second-story windows the lashes is it is 24 feet long and she puts the base of the lead 13 feet away from the house in order to avoid her flower girl that's how high up the side of the house does the Ladder reach
Answer: 20 feet
Step-by-step explanation:
in the attachment
The ladder reaches approximately 19.8 feet up the side of the house, as determined using the Pythagorean theorem.
Explanation:The question is asking us to find the height the ladder reaches up the side of the house. This is a problem dealing with right triangles and can be solved using the Pythagorean theorem, which is a^2 + b^2 = c^2, where 'a' and 'b' are the shorter sides (base and height of the house) and 'c' is the hypotenuse (the ladder).
In this case, the ladder is 24 feet long (this is our c), and the base of the ladder is 13 feet from the house (this is our a). We are trying to find b (the height of the house the ladder reaches).
Substitute these values into the Pythagorean theorem and solve for 'b':
13^2 + b^2 = 24^2
b^2 = 24^2 - 13^2
b = sqrt(24^2 - 13^2)
So, the height that the ladder reaches up the side of the house is approximately 19.8 feet.
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If you have a bank account that is modeled bybthe following equation, how much money would you have after 10 years. A=5000e 0.10t. Using the problem solving Temple with rational functions.
The money after 10 years is $ 13591.4091
Solution:
Given that,
If you have a bank account that is modeled by the following equation:
[tex]A = 5000e^{0.10t}[/tex]
To find: Money after 10 years
How much money would you have after 10 years
Substitute t = 10 in above given equation
[tex]A = 5000 \times e^{0.10 \times 10}\\\\A = 5000 \times e^{1}\\\\A = 5000 \times 2.71828\\\\A = 13591.4091[/tex]
Thus money after 10 years is $ 13591.4091
A certain solution of salt water is 10% salt and weighs 50 pounds. more salt must be added to produce a solution that is 25% salt. if x represents the pounds of salt to be added, which of the following expressions represents the number of pounds of salt in the 25% solution?
a) 0.25 (x+50)
b) 0.25x
c) 1.25 (x+50)
Answer
7.5 pounds
Step-by-step explanation:
Since adding x grams of salt will bring th percentage of the salt to 25
Hence. 10% of the 50 gram gives. 5 gram initial salt before it is added.
5+ x/ 50 * 100= 25/
5+x /50 = 0.25
5+x = 12.5
X= 12.5- 5
X= 7.5pounds
Ponderosa Paint and Glass carries three brands of paint. A customer wants to buy another gallon of paint to match paint she purchased at the store previously. She can't recall the brand name and does not wish to return home to find the old can of paint. So she selects two of the three brands of paint at random and buys them. Her husband also goes to the paint store and fails to remember what brand to buy. So he also purchases two of the three brands of paint at random. Determine the probability that both the woman and her husband fail to get the correct brand of paint. (Hint: Are the husband's selections independent of his wife's selections
The probability that both the woman and her husband fail to get the correct brand of paint is 4/9.
Explanation:To determine the probability that both the woman and her husband fail to get the correct brand of paint, we need to consider the probability of each event happening independently. Since the woman selects two brands at random out of the three available, the probability of her not getting the correct brand is 2/3. Similarly, the husband also selects two brands at random out of the three, so his probability of not getting the correct brand is also 2/3. Since the events are independent, we can multiply the probabilities together to get the probability that both fail to get the correct brand. Therefore, the probability is (2/3) * (2/3) = 4/9.
The husband's selections are independent of his wife's selections because each brand he chooses is not influenced by the brands his wife chooses. Regardless of what she selects, he still has three brands to choose from and selects two at random. This means that his probability of not getting the correct brand is the same regardless of his wife's choices.
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Evaluate 13−0.5w+6x13-0.5w+6x 13−0.5w+6x 13, minus, 0, point, 5, w, plus, 6, x when w=10w=10 w=10 w, equals, 10 and x=12x=\dfrac12 x= 2 1 x, equals, start fraction, 1, divided by, 2, end fraction .
Answer: 6x^13-1.5w+156x+13 is the answer to the first equation and is that another equation?
The expression 13 - 0.5w + 6x evaluates to 11 when substituting w=10 and x=1/2.
Explanation:The problem is to evaluate the expression 13 - 0.5w + 6x given the values w=10 and x=1/2. Following the order of operations, we first substitute the given values into the expression.
13 - 0.5(10) + 6(1/2) = 13 - 5 + 3 = 11.
The result of the evaluated expression is 11.
The US GDP (Gross Domestic Product) for 2014 was a reported 17.555 trillion dollars. The current US population is about 320 million people. Round all answers to the nearest hundredth.
Answer:
1. 1.76x10^13,
2. 3.20x10^8,
3. 5.5x10^4
Step-by-step explanation:
Answer:
Step-by-step explanation:
GDP/POPULATION
1755x10^13/3.2x10^8 = .05484x10^5
=5.484x10^4
= 5.49x10^4
Suppose you are choosing between two roads. The first route is 40 miles at 25 mph, and the second road is 65 miles at 55 mph. Which route would get you there faster, and in what amount of time?
The second route, in 1.6 hours
B. The first route, in 1.6 hours
C. The first route, in 1.18 hours
D. The second route, in 1.18 hours
Answer:
D. The second route, in 1.18 hours
Step-by-step explanation:
The appropriate relation is ...
time = distance/speed
The time required on the first route is ...
time1 = (40 mi)/(25 mi/h) = 40/25 h = 1.6 h
The time required on the second route is ...
time2 = (65 mi)/(55 mi/h) = 65/55 h = 1 2/11 h ≈ 1.18 h
__
The second route requires a shorter time, so will get you there faster. The second route will get you there in 1.18 hours.