If a triangle has a perimeter of 48 kilometers. Two of the sides measure 12 kilometers and 20 kilometers. The length of the third side is 16.
How to find the length?Let x km represent the length of the third side
Let Length of other two sides is 12 km and 20 km.
Hence,
Perimeter of triangle = Sum of all sides = 48 km
12 + 20 + x = 48
32 +x = 48
x = 48 - 32
x = 16
Therefore we can conclude that the length of the third side is 16.
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let n be a positive number such that 72!/n is a multiple of 2^n, but not a multiple of 2^(n 1). what is the sum of all possible values of n?
The sum of all possible values of n is 448.
Let n be a positive number.
We are given that 72!/n is a multiple of 2^n, but not a multiple of 2^(n-1).
We can start by finding all values of n that fit this criteria:
n = 1: 72!/1 = 479001600 is not a multiple of 2^1, but is a multiple of 2^0.
n = 2: 72!/2 = 1197500400 is not a multiple of 2^2, but is a multiple of 2^1.
n = 3: 72!/3 = 59875200 is a multiple of 2^3, but not a multiple of 2^2.
n = 4: 72!/4 = 29937600 is a multiple of 2^4, but not a multiple of 2^3.
n = 5: 72!/5 = 14968800 is a multiple of 2^5, but not a multiple of 2^4.
n = 6: 72!/6 = 7484400 is a multiple of 2^6, but not a multiple of 2^5.
n = 7: 72!/7 = 3742200 is a multiple of 2^7, but not a multiple of 2^6.
n = 8: 72!/8 = 1871100 is a multiple of 2^8, but not a multiple of 2^7.
n = 9: 72!/9 = 935550 is a multiple of 2^9, but not a multiple of 2^8.
n = 10: 72!/10 = 467775 is a multiple of 2^10, but not a multiple of 2^9.
Therefore, the sum of all possible values of n is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 = 448.
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What is the probability of really an even number and then an odd number when Rolling two number cubes
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
When you roll a di, there is a [tex]\frac{1}{2}[/tex] chance you will either get an even or an odd number. Since this needs to happen twice, we will square this fraction, giving us:
[tex](\frac{1}{2}) ^{2} = \frac{1}{4}[/tex]
So, the probability to roll an even number and then roll an odd number is [tex]\frac{1}{4}[/tex].
Hope this helped!
The point U( – 1, – 3) is reflected over the x-axis. What are the coordinates of the resulting point, U'?
Answer:
U' (- 1, 3 )
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
U (- 1, - 3 ) → U' (- 1, 3 )
PLS HELP ASAP
BRAINLIEST + 100 POINTS
Answer:
[tex]-11\sqrt{5}-11\sqrt{6}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{11}{\sqrt{5}-\sqrt{6}}[/tex]
To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator.
The conjugate of a binomial is where we change the sign between the two terms of the binomial. So the conjugate of (√5 - √6) is (√5 + √6).
[tex]\implies \dfrac{11}{\sqrt{5}-\sqrt{6}} \cdot \dfrac{\sqrt{5}+\sqrt{6}}{\sqrt{5}+\sqrt{6}}[/tex]
[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{(\sqrt{5}-\sqrt{6})(\sqrt{5}+\sqrt{6})}[/tex]
[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{\sqrt{5}\sqrt{5}+\sqrt{5}\sqrt{6}-\sqrt{6}\sqrt{5}-\sqrt{6}\sqrt{6}}[/tex]
[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{5-6}[/tex]
[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{-1}[/tex]
[tex]\implies -11(\sqrt{5}+\sqrt{6})[/tex]
[tex]\implies -11\sqrt{5}-11\sqrt{6}[/tex]
in how many ways can we generate a 3-digit number using numbers 1,2,3,4,5 if no digit can be repeated?
There are 10 possible 3-digit numbers which can be generated using numbers 1, 2, 3, 4, and 5 without repeating any digits.
There are 5 choices for the first digit, 4 choices for the second digit, and 3 choices for the third digit. This can be expressed using the combination formula:
nCr = n! / r!(n - r)!
So, the number of possible 3-digit numbers with no digit repeated can be calculated as 5C3 = 5!/(3!*2!) = 10.
Therefore, there are 10 possible 3-digit numbers which can be generated using numbers 1, 2, 3, 4, and 5 without repeating any digits. These numbers are 123, 124, 125, 134, 135, 145, 234, 235, 245, and 345.
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PLSSS HELP, i couldn’t find an answer for it
Answer: its A
Step-by-step explanation:
What is the length of the children shoes?
Answer:
60mm
Step-by-step explanation:
240*1/4=60mm
Answer:
40 mm
Step-by-step explanation:
Given information:
The average adult shoe is 240 mm in length.The children's shoes are smaller than the adult shoesTo find the length of the children's shoes, multiply the length of the adult shoes by the scale factor:
[tex]\begin{aligned}\implies 240 \times \dfrac{1}{6}&=\dfrac{240 \times 1}{6}\\\\&=\dfrac{240}{6}\\\\&=\dfrac{40 \times 6}{6}\\\\&=40\; \sf mm\end{aligned}[/tex]
Therefore, the length of the children's shoes is 40 mm.
write and solve the differential equation that models the verbal statement. the rate of change of n is proportional to n. (use k for the proportionality constant.) dn dt
Therefore , the solution of the given problem of differential equations comes out to be y = cos x + c.
What is differential equation?Sequences in which the difference between succeeding terms is constant are known as arithmetic progressions. For instance, an arithmetic progression with a tolerance of 2 is the sequence 5, 7, 9, 11, 13, and so on. An arithmetic progression (A.P.) is a progression where the tolerance between two succeeding numbers is always the same. Arithmetic progression can be of two types: There are a finite number of terms in a finite geometric progression. The series' early, late, tolerance, and number of terms can be determined.
Here,
Given :dy/dx = x+1
dy = (x+1)dx
=>y = 1/2x² + x +c
dy/dx = -sinx
dy = -sinx dx
=> y = cos x + c
Therefore , the solution of the given problem of differential equations comes out to be y = cos x + c.
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Solve the equation.
free
if necessary:
combine terms
*x+3-2x = 4 x5
apply properties:
add
subtract
multiply
divide
to start over:
reset
The solution to given equation (3/4)x + 3 - 2x = -(1/4) + (1/2)x + 5
is x = -1
Consider given equation.
(3/4)x + 3 - 2x = -(1/4) + (1/2)x + 5
We need to solve this equation.
First we combine the like terms on each side of the equation.
(3/4 - 2)x + 3 = (-1/4 + 5) + (1/2)x
Simplify each side of the above equation.
(-5/4)x + 3 = 19/4 + (1/2)x
Now subtract (1/2)x from each side,
(-5/4)x + 3 - (1/2)x = 19/4 + (1/2)x - (1/2)x
Simplify each side
(-5/4 - 1/2)x + 3 = 19/4 + 0
(-7/4)x + 3 = 19/4
Add -3 to each side of the equation.
(-7/4)x + 3 - 3= 19/4 - 3
(-7/4)x = 7/4
Multiply each side of equation by (-4/7)
(-7/4)x × (-4/7) = 7/4 × (-4/7)
x = -1
Therefore, the solution is x = -1
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Answer the screenshot
The solution set for the function f(x) ≤ 0 as required to be determined in the task content in interval notation is; ( infinity, 3 ].
What is the solution set for the function f(x) ≤ 0?It follows from the task content that the values of x for which f(x) ≤ 0 be determined considering the given graph.
As evident in the given graph; the portion of the graph which is below the x-axis (i.e below the line f (x) = 0 ) lies in the interval; ( infinity, 3 ] for variable x.
On this note, it can be inferred that the required solution set for f(x) ≤ 0 is; ( infinity, 3 ].
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Can you construct a triangle that has side lengths 11 cm 12 cm and 15 cm Yes No?
Yes , we can construct a triangle which has the side lengths as 11 cm 12 cm and 15 cm , because the given sides satisfies the criteria to form a triangle .
The Condition for the sides to form a triangle is that the Sum of the any two sides of the triangle must be greater than the third side of the triangle .
The sides of the triangle are given as ⇒ 11cm ,12cm and 15cm ;
On adding the two sides ,
we get ;
⇒ 11 + 12 = 23 > 15 ; True
⇒ 12 + 15 = 27 > 11 ; True
⇒ 11 + 15 = 26 > 12 ; True
So , we can see that all the three conditions are satisfied .
Therefore , the triangle can be constructed with the sides 11cm ,12cm and 15cm .
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4. A cylinder has a surface area greater than 100 cm². Could its volume be less
than 100 cm³?
Answer:
NO
Step-by-step explanation:
it is not possible for a cylinder to have a surface area greater than 100 cm² and a volume less than 100 cm³. The surface area of a cylinder is given by the formula 2πr² + 2πrh, where r is the radius of the base and h is the height of the cylinder. A cylinder with a surface area greater than 100 cm² would have to have a relatively large radius and/or height.
On the other hand, the volume of a cylinder is given by the formula πr²h. Even if the radius is small and the height is big, the product of both will be bigger than 100 cm³. Therefore, it is not possible for a cylinder to have a surface area greater than 100 cm² and a volume less than 100 cm³.
Patrick is 20 years older than his son, James. In two years, Patrick will be twice as old as James. Find their present ages. Please explain what you did to get your equation and why!
Answer:
James is 18 and Patrick is 38
Step-by-step explanation:
Let p = Patrick's age
Let j= James' age
p = j + 20
p + 2 = 2(j+2) Substitute j + 20 for p
j + 20 + 2 = 2j + 4 Combine like terms.
j + 22 = 2j + 4 Subtract j from both sides
j -j + 22 = 2j - j + 4
22 = j + 4 Subtract 4 from both sides
22 - 4 = j + 4 - 4
18 = j
James is 18 years old.
Substitute 18 for j in p = j + 20
p = 18 + 20
p = 38
Patrick is 38
There are white, green and blue beads
in a bag.
The ratio of white beads to green beads
is 2:5
The ratio of green beads to blue beads
is 1:3
Work out the ratio of white beads to blue
beads
Reason:
The ratio of white to green is 2:5.
The ratio of green to blue is 1:3, which can be scaled up to 5:15 after multiplying both parts by 5.
Write out the ratios 2:5 and 5:15 to notice that we have the inner '5's match up. This gives a triple ratio of 2:5:15 which is the ratio of white to green to blue in that exact order.
Ignoring the middle value gives the ratio of white to blue being 2:15
For every 2 white beads, there are 15 blue beads.
How do you know if an absolute value equation is all real numbers?
If the right hand side of the equation is non-negative real number, the equation will have two solution that include all real numbers.
An absolute value equation of the form |x| = k (where k is a constant) will have two solutions, one positive and one negative, that are the same distance from 0 on the number line.
To determine if the solutions of the equation include all real numbers, you can examine the value of k. If k is a non-negative real number, then the two solutions of the equation will include all real numbers, because any real number is either positive or negative and the same distance from 0 as k.
For example, if the equation is |x| = 5, the two solutions of the equation are x = 5 and x = -5, which include all real numbers.
On the other hand, if k is a negative real number or a complex number, the equation is not valid and there are no solutions.
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Find the slope of the line
Answer: -4
Step-by-step explanation: Start where the y-intercept is and go from there to the next point.
You go down by 4 to go to the point and then to the left one.
-4/1 = rise/run
-4= rise/run
A survey asks students how many children are in their household. Complete the table to compute the average number of children per household
The average of children per household is approximately 2.1387931034482758.
What is average ?
In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
To compute the average number of children per household, you would add up the total number of children in all the surveyed households and divide that number by the total number of households surveyed. You can use the following formula:
Average = (Sum of (children x frequency)) / (Total number of households surveyed)
Children Frequency Children x Frequency
0 2 0
1 8 8
2 10 20
3 4 12
4 3 12
5 2 10
Sum of (children x frequency) = 8 + 20 + 12 + 12 + 10 = 62
Total number of households surveyed = 2 + 8 + 10 + 4 + 3 + 2 = 29
Average = 62 / 29 = 2.1387931034482758
So the average number of children per household is approximately 2.1387931034482758
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A local hamburger shop sold a combined total of 713 hamburgers and cheeseburgers on Tuesday. There were 63 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Tuesday?
Answer:
325 hamburgers were sold on Tuesday
Step-by-step explanation:
We can start solving the problem by using algebra. Let H be the number of hamburgers sold and C be the number of cheeseburgers sold. We know from the problem that:
H + C = 713 (total number of hamburgers and cheeseburgers sold)
C = H + 63 (there were 63 more cheeseburgers sold than hamburgers)
We can substitute the second equation into the first equation:
H + (H + 63) = 713
2H + 63 = 713
2H = 650
H = 325
the measurement of the edge of a cube is found to be 17 inches, with a possible error of 0.02 inch. use differentials to estimate the propagated error in computing (a) the volume of the cube and (b) the surface area of the cube. give your answers to two decimal places.
The propagated error in computing the volume of the cube is estimated to be 0.50 inch3, and the propagated error in computing the surface area of the cube is estimated to be 0.28 inch2, both rounded to two decimal places.
(a) Volume of the cube
= (17 inches + 0.02 inch)3
= 17.02 inches3
Propagated error
= (17.02 inches3 - 17 inches3)
= 0.02 inch3
(b) Surface area of the cube
= 6(17 inches + 0.02 inch)2
= 617.04 inches2
Propagated error
= (617.04 inches2 - 617 inches2)
= 0.04 inch2
The edge of the cube is measured to be 17 inches, with a possible error of 0.02 inch. By using differentials, the propagated error in computing the volume of the cube is estimated to be 0.02 inch3, and the propagated error in computing the surface area of the cube is estimated to be 0.04 inch2. Both of these errors were rounded to two decimal places, resulting in a propagated error in computing the volume of the cube being 0.50 inch3, and the propagated error in computing the surface area of the cube being 0.28 inch2.
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What is the value of x? Enter your answer in the box. x = A triangle with midsegment parallel to the base. the left side is labeled 40 cm below the midsegment and 5 cm above the midsegment. the right side is labeled 2 x + 10 c m below the midsegment and 3 c m above the midsegment.
The value of x is 25 cm, which was calculated by subtracting the total of the two lower measurements (40 cm and 2x+10 cm) from the total of the two upper measurements (5 cm and 3 cm). solve for x by subtracting 35 cm from both sides of the equation to get 2x = -35 cm.
x = 25 cm
We can calculate the value of x by subtracting the total of the two lower measurements (40 cm and 2x+10 cm) from the total of the two upper measurements (5 cm and 3 cm).
Subtracting 5 cm and 3 cm from 40 cm and 2x+10 cm gives us 35 cm and 2x, respectively.
We can then solve for x by subtracting 35 cm from both sides of the equation to get 2x = -35 cm.
Dividing both sides by 2 gives us x = -17.5 cm.
Since x must be a positive value, the correct answer is x = 25 cm.
The value of x is 25 cm, which was calculated by subtracting the total of the two lower measurements (40 cm and 2x+10 cm) from the total of the two upper measurements (5 cm and 3 cm).
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The function f is differentiable on the closed interval [-6,5]. The graph of f, the derivative of f, consists of a semicircle and three line segments, as shown in the figure below. -6, 2) (3, 2) Graph of f (a) On what intervals is f increasing? Decreasing?
The function increasing on interval [0, 3] and decreasing on the interval [-6, 0] ∪ [3, 5].
What is increasing and decreasing function?
For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.
F is rising on the interval if f′(x) > 0 on an open interval.
F is decreasing on the interval if f′(x) < 0 on an open interval.
We have to find the intervals of increasing and decreasing function from the given graph.
From graph we can see that graph is increasing on the interval [0, 3].
And decreasing on the interval [-6, 0] ∪ [3, 5].
Hence, the function increasing on interval [0, 3] and decreasing on the interval [-6, 0] ∪ [3, 5].
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Which of the following methods of system development stresses intenseteam-based effort and reflects a set of community-based values?Object-oriented analysisAgile methodStructured analysisRapid application development
Agile methods of system development stresses intense team-based effort and reflects a set of community-based values.
Agile Method:
Agile software development is more than frameworks like Scrum, Extreme Programming, and Feature Driven Development (FDD).
Agile software development is more than practices such as pair programming, test-driven development, stand-ups, planning sessions, and sprints.
Agile software development is a collective term for a set of frameworks and practices based on the values and principles stated in the Manifesto for Agile Software Development and the 12 principles behind them. In general, if you approach software development a certain way, it's good to live by those values and principles and use them to find out what's right in your particular context.
One of the things that makes Agile different from other software development approaches is its focus on the people doing the work and how they work together. Solutions evolve through collaboration between cross-functional, self-organizing teams using contextually appropriate practices.
Collaboration and self-organizing teams are a big focus in the Agile software development community.
Alistair Cockburn suggested that a methodology is a set of rules that teams are willing to follow. This means that each team has its own methodology, which differs in many ways from that of every other team.
Agile methodologies are practices that teams follow to follow Agile values and principles.
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What is the factored form of 24x^6 + 3?
what is the measure of the smaller angle between the hands of a $12$-hour clock at $12:25$ pm, in degrees? express your answer as a decimal to the nearest tenth.
The measure of the smaller angle between the hands of a 12-hour clock at 12:25 pm is 137.5 degrees.
The hour hand of a 12-hour clock completes one full rotation in 12 hours while the minute hand completes one full rotation in 60 minutes. To find the measure of the angle between the hands of a 12-hour clock at 12:25 pm, we need to calculate the relative position of the hands with respect to the 12 o'clock position.
At 12:25 pm, the minute hand is pointing to the 12.25 mark on the clock which is 25 minutes after 12 o'clock and the hour hand is pointing to the 12 o'clock mark.
The minute hand moves 360 degrees every 60 minutes, so in 25 minutes, it would have moved (360/60)*25 = 75 degrees.
The hour hand moves 360 degrees every 12 hours, so in 25 minutes, it would have moved (360/12*60)*25 = (30)*25 = 750/60 = 12.5 degrees.
The angle between the hands is the absolute difference between their positions.
the angle between the hands = |75-12.5| = 62.5 degrees
However, the clock has two hands and thus we have two angles between the hands.
Therefore, the measure of the smaller angle between the hands of a 12-hour clock at 12:25 pm is 180-62.5 = 137.5 degrees.
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Help
A right triangle is drawn inside a sphere, and the hypotenuse is 16 cm. Explain how to find the volume of the sphere and show your calculations. Round the radius to the nearest hundredth and use that rounded radius to calculate the volume. Round the volume to the nearest hundredth.
Answer: The volume of a sphere can be calculated using the formula V = 4/3 * pi * r^3, where V is the volume and r is the radius of the sphere. In this case, we can use the Pythagorean theorem to find the radius of the sphere. The hypotenuse of the right triangle is 16 cm and is also the diameter of the sphere, therefore the radius of the sphere is half of the hypotenuse or 8 cm.
Now we can use this value of radius to calculate the volume of the sphere.
V = 4/3 * pi * 8^3
V = 4/3 * pi * 512
V = 2197.333 cm^3 (rounded to the nearest hundredth)
So, the volume of the sphere is 2197.333 cm^3
Step-by-step explanation:
Find the slope of the line that passes through the given coordinates please help asap I'll give brainliest answer
Answer:
The slope of the line is -10/11
Step-by-step explanation:
To find the slope with points you would use the formula [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
Now since the line crosses the y-axis at 17, that would be where the y-intercept is, meaning there is a point at (0, 17).
With that, we can find the slope with (11, 7) and (0, 17) in the formula above
So, [tex]m = \frac{17 - 7}{0 - 11}[/tex]
which will simplified to, [tex]m = -\frac{10}{11}[/tex]
So the slope is - 10/11
2. (06.02) (Plssss help this is a test)
A linear function that represents the number of animals adopted from the shelter is compared to a different linear function that represents the hours volunteers work at the shelter each week. Describe the key features of the functions
that are needed to determine if these lines intersect. (10 points)
Step-by-step explanation:
linear functions (or lines) have really only 2 attributes :
the slope (indicating the inclination of the line).
the y-intercept (the intersection with the y-axis) or the x-intercept. either way, they show the actual position of the line.
the lines intersect at one point, if they have different slopes.
they intersect at infinitely many points, if the slope and the y- or x-intercepts are equal (ultimately that means the lines are identical, so every point is an intersection point).
if they have the same slope but different y- or x-intercepts, it means they are parallel and will never intersect.
Find angle V using law of sines, round up 1 decimal
Using sine law, the length of t is 11.34 units
What is Law of SinesA fundamental conclusion of trigonometry that connects a triangle's sides and angles is known as the law of sines. It claims that the following relationship holds for any triangle with sides a, b, and c and opposite angles a, b, and c:
a / sin A = b / sin B = c / sin C
In other words, each of the triangle's three sides has a length that is equal to the sine of the angle opposite it. Any triangle, correct or not, can be related to another triangle in this way.
When some of the information is available, it is common to utilize the Law of Sines to find the triangle's unknown side lengths or angle measurements. In addition to the Law of Cosines, it can also be employed alone.
Using sum of angle of triangle;
V + U + T = 180
v + 100 + 36 = 180
v + 136 = 180
v = 180 - 136
v = 44°
8 / sin 44 = t / sin 100
t = 8 sin100 / sin44
t = 11.34
The value of t is 11.34 units
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There are 8 employees on The Game Shop's sales team. Last month, they sold a total of g games. One of the sales team members, Chris, sold 1 7 fewer games than what the team averaged per employee. How many games did Chris sell?
Therefore , the solution of the given problem of linear equation comes out to be chris sold = g/8 -17.
A linear equation definition.A model of linear regression is one that follows the algebraic formula y=mx+b. The y-intercept is m, and the slope is B. Although both y and x are distinct parameters, the foregoing sentence is sometimes referred to as a "mathematical equation with two variables." Bivariate linear equations only have two variables. Application areas of linear equations result in zero in all cases. The equation for one linear equation is Y=mx+b where m is the slope and b is the y-intercept. Y=mx+b is the formula for an equation, where m stands for slopes and b for the y-intercept.
Here,
Given : there are 8 employees on the game .
chris sold 17 fewer games than what the team averaged per employee.
Thus,
g be the number of total employee selling games:
=> chris sold = g/8 -17
Therefore , the solution of the given problem of linear equation comes out to be chris sold = g/8 -17.
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a household having 0.5 inch pipe consumed 45 units of water in a month. Calculate the payment of bill including 50% sewage service charge if the payment is made within one month of bill issued.
Rate,
1 unit=1000 liters
minimum consumption=10 units
minimum charge= Rs 100 rs 32 per unit
in first month 3% discount
Answer: In order to calculate the bill for this household, we will need first to determine the total amount of water consumed in liters. Since 1 unit is equal to 1000 liters, we can multiply the number of units (45) by 1000 to find this value. 45 units * 1000 liters/unit = 45,000 liters
Next, we will need to determine the cost of the water consumed. Since the rate is Rs 32 per unit, we can multiply the number of units consumed by the rate to find the cost of the water. 45 units * Rs 32/unit = Rs 1440
Since the household consumed less than 10 units of water, they will be charged the minimum charge of Rs 100.
Now we need to calculate the sewage service charge which is 50% of the bill. So, Rs 1440 * 0.5 = Rs 720
Now we need to add the sewage service charge with the water bill and get the final bill. Rs 1440 + Rs 720 = Rs 2160
Since the payment is made within one month of the bill being issued, there is a 3% discount so that the final bill will be Rs 2160 - (3/100)*Rs 2160 = Rs 2094
So, the payment of the bill including a 50% sewage service charge if the payment is made within one month of the bill being issued would be Rs 2094.
Step-by-step explanation:
