Given statement: Here's the table with the values organized:
X | Y
-----
1 | 5
-3 | 2
7 | 2
6 | 3
7 | -4
5 | 9
8 | 4
1 | 7
1 | 0
This statement is False.
Because, The table provided is not a function because it does not have a clear and unique output value for each input value.
Since the X values 1 and 7 have multiple Y values, the given table is not a function.
In a function, each input value (X) must have a unique output value (y). However, in the given table, there are some input values, such as X = 7 and X = 1, that have multiple output values. For example, when X = 7, the table provides two output values, 2 and -4. Similarly, when X = 1, the table provides two output values, 5 and 0.
A function is a mathematical relationship between the input and output values, where each input value produces only one unique output value. Functions are used to represent many real-world scenarios, including calculating distances, temperatures, and profits. Therefore, it is crucial to ensure that the provided table represents a function by ensuring that each input value has a unique output value.
In conclusion, the table provided is not a function as it violates the one-to-one mapping between input and output values.
A function must have a clear and unique output value for each input value.
To determine if the given table represents a function, we need to make sure that each input (X value) corresponds to only one output (Y value).
Now let's check for any repeating X values with different Y values:
1 corresponds to both 5 and 7
7 corresponds to both 2 and -4.
False.
For similar question on value.
https://brainly.com/question/27882730
#SPJ11
Owen's Muffin Extravaganza recorded how many of each type of muffin it recently sold.
bran muffins 25
blueberry muffins 12
poppy seed muffins 3
chocolate chip muffins 10
Considering this data, how many of the next 16 muffins sold would you expect to be bran muffins?
The requried, we would expect 8 of the next 16 muffins sold to be bran muffins.
Out of a total of 50 muffins sold, 25 were bran muffins. That means that the proportion of bran muffins to total muffins sold is:
25 / 50 = 1/2
To find how many of the next 16 muffins sold would be bran muffins, we can multiply the proportion of bran muffins by the total number of muffins:
(1/2) * 16 = 8
Therefore, we would expect 8 of the next 16 muffins sold to be bran muffins.
Learn more about proportions here:
https://brainly.com/question/31013500
#SPJ1
HELP HELP NOW.BRO PLEASE. Benjamin is planning what to wear tomorrow evening.
• He has 3 shirts to choose from: red, white, and green.
• He has 2 pairs of pants to choose from: blue jeans and khaki pants.
• He has 3 pairs of shoes to choose from: sneakers, flip flops, and boots.
Benjamin randomly chooses one item from each group. What is the probability that he chooses
sneakers and the green shirt?
Answer:1/9 i gotchu
Step-by-step explanation:
Answer:
4/8
Step-by-step explanation:
List two reason why do you think the given questionnaire i not suitable
Some of the general reason why questionnaire are often not suitable for a study includes:
being ambiguous or have unclear questions: being biased or have leading questionsWhat problems makes questionnaire unsuitable for a study?If the questions in the questionnaire are unclear or open to interpretation, then the results may not be accurate or useful. Respondents may answer questions differently based on their own interpretation, leading to inconsistent or unreliable data.
Also, if the questions in the questionnaire are biased, then, the results may be skewed towards a particular outcome or viewpoint. Respondents may feel pressured or influenced to answer questions in a certain way, rather than providing their honest opinion and this can lead to inaccurate or unrepresentative data.
Read more about questionnaire
brainly.com/question/6285776
#SPJ1
Find One third and one fifth of the Following (A) 1/3 of 33 and 1/3 of 1/5 of 45
one third of 33 is 11
one fifth of 45 is 9.
Suppose a standard six sided die is rolled 15 times. What is the probability of rolling 1 exactly 4 times? Round to four decimal places.
Therefore , the solution of the given problem of probability comes out to be rounded to four decimal places, is approximately 0.1041.
What precisely is probability?The assessment of the probability that a claim is true or that a particular event will happen is the main objective of the constructions inside style known as criteria. Chance can be symbolised by any number between zero and 1, for which 1 typically denotes certainty range and 0 typically denotes possibility. A probability diagram illustrates the likelihood that a particular occurrence will take place. Decimal digits 0, 1, rationals with just 0% and roughly 100%.
Here,
A typical six-sided die has a 1/6 chance of rolling a 1 on any particular roll.
We can describe this scenario using a binomial distribution with
=> n = 15 and p = 1/6 since we are rolling the die 15 times.
The binomial probability formula can be used to calculate the likelihood of rolling precisely four ones:
=> P(X = 4) = (15 choose 4) (15 choose 4) * (1/6)^4 * (5/6)^11
Calculating the answer, we obtain:
=> P(X = 4) ≈ 0.1041
The likelihood of rolling precisely four one-sided dice, rounded to four decimal places, is approximately 0.1041.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
write the equation of the line slope 4 and y intercept 1/2
Answer:
y = 4x + 1/2
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
We know
m = 4
b = 1/2
So, the equation is y = 4x + 1/2
matthew is on the basketball team at school. she calculated it hat in 65 minutes he can burn 468 calories. if m is the number of minutes and c is the number of calories burned
Answer:
7.2
Step-by-step explanation:
468/65 = 7.2
What are the coordinates of point A(-22, 1) after it is reflected across the x-axis?
O A) (22,1)
O B) (1.-22)
oc) (23,-1)
OD) (-2,-1)
The required correct answer is (D) (-22, -1).
What is reflected across the x-axis?By graphing y=-f(x), we can reflect the graph of any function f about the x-axis, and by plotting y=f, we can reflect the graph about the y-axis.(-x). By graphing y=-f, we can even mirror it about both axes.(-x).
According got question:When a point is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same.
Therefore, to find the coordinates of point A after it is reflected across the x-axis, we change the sign of the y-coordinate of A.
So, if the original coordinates of point A are (-22, 1), the coordinates of A after it is reflected across the x-axis are (-22, -1).
Therefore, the correct answer is (D) (-22, -1).
To know more about Coordinates visit:
brainly.com/question/29189189
#SPJ1
[tex]2.3x^{2} +\frac{69}{465} =?[/tex]
Answer: To solve this expression, we need to simplify it using the order of operations (PEMDAS) and perform the indicated operations:
2.3x^2 + 69 / 465
First, we need to simplify the fraction 69/465. Both the numerator and denominator have a common factor of 3, so we can simplify the fraction by dividing both by 3:
69 / 465 = 23 / 155
Now we can substitute this simplified fraction back into the original expression:
2.3x^2 + 23 / 155
The expression is now in simplified form, and there are no more operations we can perform. So this is the final answer.
Alternatively, if the expression was meant to be solved for x, we would need an equation (e.g., 2.3x^2 + 69 / 465 = some value) in order to solve for x. As it stands, we cannot solve for x with the given expression.
Step-by-step explanation:
Find the area of Length = 15 m, breadth = 9 m
Answer:
135 square meters
Step-by-step explanation:
Area = Length x Breadth
15 m x 9 m = 135 square meters.
Answer:
135m
Step-by-step explanation:
l×b = Area
15×9 = 135m
Find the area of the figure below.
Answer:
348 in²
Step-by-step explanation:
[tex] \frac{ad \times (cd + ab)}{2} [/tex]
[tex] \frac{19.2(16 + 24)}{2} [/tex]
384 in²
Prove that the roots of x² + (1-k)x+k-3=0 are real for all real values of k.
Answer:
Step-by-step explanation:To prove that the roots of the equation x² + (1-k)x + k-3 = 0 are real for all real values of k, we need to show that the discriminant of the equation is non-negative for all values of k.
The discriminant of a quadratic equation ax² + bx + c = 0 is given by b² - 4ac. If the discriminant is positive, then the equation has two distinct real roots; if it is zero, then the equation has one real root (a repeated root); and if it is negative, then the equation has no real roots.
So, in this case, the discriminant of the equation is:
(1-k)² - 4(1)(k-3)
= 1 - 2k + k² - 4k + 12
= k² - 6k + 13
We need to show that k² - 6k + 13 ≥ 0 for all real values of k.
To do this, we can complete the square:
k² - 6k + 13
= (k - 3)² + 4
Since the square of any real number is non-negative, we have (k-3)² ≥ 0 for all k, which means that (k-3)² + 4 ≥ 4.
Therefore, k² - 6k + 13 ≥ 4 for all real values of k, which means that the discriminant of the quadratic equation x² + (1-k)x + k-3 = 0 is non-negative for all real values of k. Hence, the roots of the equation are real for all real values of k.
(ii) Find Z if -18=Z-3+2Z
Answer: Z=-5
Step-by-step explanation:
we want to group Z on only one side of the equation
-18=Z-3+2Z
-18-Z-2Z=-3 (subtract Z and 2Z from both sides, to remove Z from one side and to move it to the other side)
-3Z=-3+18 (regroup Z and add 18 on both sides, to have Z on only one side)
-3Z=15 (add -3+18)
3Z=-15 (multiply both sides by -1 to get a positive Z)
Z=-5 (divide both sides by 3)
Solve the IVP: y′′+ 2y′= [tex]\frac{1}{e^{2t}-1}[/tex], y(−ln 2) = 0, y′(−ln 2) = ln(9/8).
According to the question the solution to the given IVP is [tex](ln(9/8))(e^{2t} - te^{2t} + 1).[/tex]
What is IVP?IVP stands for Initial Value Problem. It is a mathematical problem where an initial value is given at a certain point in time, and the goal is to find the solution for the function at all other points in time. An IVP is important in the study of differential equations, which are used to model a wide range of phenomena in science, engineering, and economics.
The given IVP is a second order linear differential equation with constant coefficients, so the general solution can be written as
[tex]y(t) = c_1e^{2t} + c_2te^{2t} + d[/tex]
where c_1, c_2, and d are constants to be determined.
Substituting the initial conditions into the general solution yields
[tex]y(-ln2) = c_1(-ln2)^2 + c_2(-ln2) + d = 0[/tex]
and
[tex]y'(-ln2) = 2c_1(-ln2) + c_2e^{2(-ln2)} = ln(9/8).[/tex]
Solving these two equations for c_1 and c_2 yields
[tex]c_1 = -(ln(9/8) + d)/2(-ln2)^2[/tex]
and
[tex]c_2 = (ln(9/8) + 2d)/2(-ln2)[/tex]
Substituting these values into the general solution and solving for d yields
d = ln(9/8).
Therefore, the solution to the given IVP is
[tex]y(t) = -(ln(9/8) + ln(9/8))e^{2t}/2(-ln2)^2 + (ln(9/8) + 2ln(9/8))te^{2t}/2(-ln2) + ln(9/8)[/tex]
= [tex](ln(9/8))(e^{2t} - te^{2t} + 1).[/tex]
To learn more about IVP
https://brainly.com/question/28362873
#SPJ1
2 A fisherman catches 30 fish during a particular day.of the fish weigh more than 2 kg. He can sell each of these fish for £5.99. The remaining fish are sold to a pet food manufacturer at 75% of the price.
translate this phrase into an algebraic expression.
The sum of 15 and twice Jose’s score
use the variable j to represent Jose’s score
Answer:
15 + 2j
Step-by-step explanation:
Sum, which means addition, is used to say that 15 will be added to something.
That "something" is twice Jose's score, which is 2 * j, since j is the score.
15 + 2 * j, or just 15 + 2j
45°, 35.8°, x°
Find the missing measure with the given measure
Answer:
a = 45 b = 35.8 c = 57.503
Step-by-step explanation:
there
A pyrotechnician plans for two fireworks to explode together at the same height in the air. They travel at speeds shown below. Firework B is launched 0.25 s before
Firework A. How many seconds after Firework B launches will both fireworks explode?
Firework A : 320 ft/s
Firework B : 220 ft/s
Both fireworks will explode ___ seconds after Firework B launches.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)
Both fireworks will explode at time 0.55 seconds after Firework B launches.
What is distance?Distance is a unit of measurement for the separation between two places. This scalar number is typically expressed in terms of metres, feet, or miles. Depending on the situation, other distance formulae can be used, such as the geometry distance formula or the physics average speed formula. Displacement, a vector quantity that considers the direction of motion, is distinct from distance. Distance is the overall length of an object's route, whereas displacement is the change in an object's location from its beginning position to its end position.
Let us suppose time = t.
Given that, Firework B is launched 0.25 s before Firework A.
Time taken for Firework A to explode after Firework B launches is t - 0.25.
The distance traveled by each firework is given by:
Distance of Firework A = 320t
Distance of Firework B = 220(t - 0.25) = 220t - 55
Since both fireworks explode at the same height, their distances traveled must be equal. Therefore:
320t = 220t - 55
100t = 55
t = 0.55 seconds
Hence, both fireworks will explode 0.55 seconds after Firework B launches.
Learn more about distance here:
https://brainly.com/question/15256256
#SPJ1
a scientist is conducting experiments on two bacteria cultures. the table shows the functions representing the growth rate of each bacteria culture, where x represents the number of days since the start of the experiment, and x>(or equal to) 0
A. 2.9 Days
B.5.8 Days
C.36.6 Days
D. 106.0 Days
The approximate value of x which the number of bacteria would approximately be the same include the following: A. 2.9 Days.
What is an exponential function?In Mathematics, an exponential function can be represented or modeled by using the following mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represent the base value, vertical intercept, or y-intercept.b represent the slope or rate of change.x represent time.Based on the information provided about the two bacteria cultures, we can logically deduce the following exponential functions;
[tex]y = 100(1.02)^x \\\\y = 80(1.05)^{2x}[/tex]
By equating the two exponential functions above, we have:
[tex]100(1.02)^x = 80(1.05)^{2x}\\\\\frac{1.02^x}{1.05^{2x}} =80/100\\\\\frac{1.02^x}{1.1025^{x}} =0.8\\\\0.9252^x = 0.8[/tex]
By taking the logarithm of both sides, we have:
[tex]Log_{0.9252}(0.9252^x) = Log_{0.9252}(0.8)[/tex]
x = 2.9 days.
Read more on exponential functions here: https://brainly.com/question/30241796
#SPJ1
The function f(x) = 2x3 - 6x2 _ 210x + 7 is increasing on the inverval
(-00, A]U |B, ∞), and decreasing on the interval [4, B].
A =
and B =
The critical points are A = -5 and B = 7, and the function is increasing on the interval (-∞, -5] ∪ [7, ∞), and decreasing on the interval [-5, 7].
What is the value of A and B along the intervalTo find A and B, we need to find the critical points of the function f(x) and determine the intervals of increase and decrease.
First, we find the derivative of f(x) as:
f'(x) = 6x^2 - 12x - 210
Next, we find the critical points by setting f'(x) = 0:
6x^2 - 12x - 210 = 0
Simplifying, we get:
x^2 - 2x - 35 = 0
Factoring, we get:
(x - 7)(x + 5) = 0
So the critical points are x = 7 and x = -5.
Now we can determine the intervals of increase and decrease. We create a sign chart based on the sign of f'(x) in each interval:
Interval | f'(x) | f(x) increasing/decreasing
(-∞, -5) | - | decreasing
(-5, 7) | + | increasing
(7, ∞) | - | decreasing
Learn more on critical points here;
https://brainly.com/question/30760896
#SPJ1
The graph of the function g(x) contains the point (5, 1/3). What point must be on the graph of y = 3g(x + 1)?
Answer: we move (5, 1/3) to (5-3, 1/3*3) = (2, 1)
Step-by-step explanation:
Find the area of the figure below, formed from a triangle and a parallelogram. one triangle has a height of 3mm. Another triangle has a side of 4mm and 5mm. the trapezoid has a side of 5mm, 5mm and height of 4mm.
After answering the presented question, we can conclude that As a triangle result, the figure has a surface area of 24.5 square millimeters.
What precisely is a triangle?Because it has four or more pieces, a triangle is a polygon. It has a straightforward rectangular shape. A triangle ABC is a rectangle with A, B, and C edges. Euclidean geometry provides a single plane and cube when the sides are not collinear. A polygon is a triangle with three components and three angles. The corners of a triangle are the spots where the three edges meet. A triangle's sides add up to 180 degrees.
To calculate the area of the figure, we must first calculate the areas of each shape and then add them together.
c² = a² + b²5² = 4
_g² +b²25 = 16+ b²_9_ = 3
As a result, the base of the second triangle is 3mm. We can now pinpoint its location:
A = 1/2 * 3mm * 3mm * 3mm = 4.5mm2
A is equal to (5mm + 5mm) * 4mm / 2 = 20mm2.
We can now add the regions of all three shapes:
Total surface area = 4.5mm2 + 20mm2 = 24.5mm2
As a result, the figure has a surface area of 24.5 square millimeters.
To know more about triangle visit:
brainly.com/question/2773823
#SPJ1
At the Chesterfield Pet Adoption Day, there are 5 tents set up where people can play with puppies and senior dogs. In each tent, there are x puppy playpens and y senior dog playpens. There are 4 dogs in each playpen. Pick all the expressions that represent how many dogs are at the event.
Answer: The total number of dogs at the event will depend on the number of playpens in each tent and the number of tents.
In each tent, there are x puppy playpens and y senior dog playpens, and there are 4 dogs in each playpen.
To find the total number of dogs at the event, we need to multiply the number of playpens in each tent by the number of dogs per playpen, and then multiply that by the number of tents.
So the expressions that represent the total number of dogs at the event are:
5xy(4) (multiplying the number of playpens in each tent by the number of dogs per playpen, and then by the number of tents).
20xy (combining the multiplication).
4(5xy) (multiplying the number of dogs per playpen by the number of playpens in each tent, and then by the number of tents).
20xy (combining the multiplication).
Therefore, the expressions that represent the total number of dogs at the event are 20xy and 4(5xy).
Step-by-step explanation:
The number of puppies at the event is represented by the expression 20x, and the number of senior dogs at the event is represented by the expression 20y.
Explanation:The total number of dogs at the event can be calculated by adding the number of puppies and senior dogs. Since there are x puppy playpens and y senior dog playpens in each tent, and there are 5 tents, we would have 5 * x playpens for puppies and 5 * y playpens for senior dogs. Each playpen holds 4 dogs, so the number of puppies would be 4 * 5 * x, and the number of senior dogs would be 4 * 5 * y. Therefore, the expressions that represent the total number of dogs at the event are 20x (for the puppies) and 20y (for the senior dogs).
Learn more about Expression here:https://brainly.com/question/34132400
#SPJ2
NO LINKS!!! URGENT HELP PLEASE!!!
Please help me with #20, 22, and 24
Answer:
see the work below
Step-by-step explanation:
20.) x = √32²+32² = √2048 = 45.25
y = 32(sin60) = 27.7
z = 32(cos60) = 16
22.) x = 7√3 / cos60 = 24.25 = 14√3
y = 14√3 / tan30 = 42
sin30 = 14√3 / (z+7√3)
z + 7√3 = 14√3 / sin30
z = 14√3/√sin30 - 7√3 = 36.37 = 21√3
24.) z = 18(tan30) = 10.4
h = √10.4² + 18² = √432 = 20.785
x = y
2x² = 20.785²
x = √20.785²/2 = 14.7
y = 14.7
Answer:
Question 20:
x = 32√2 unitsy = 16√3 unitsz = 16 unitsQuestion 22:
x = 14√3 unitsy = 42 unitsz = 21√3 unitsQuestion 24:
x = 6√6 unitsy = 6√6 unitsz = 6√3 unitsStep-by-step explanation:
45-45-90 triangleA 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2. Therefore, the formula for the ratio of the sides is b : b : b√2 where:
b is each side opposite the 45 degree angles (legs).b√2 is the side opposite the right angle (hypotenuse).30-60-90 triangleA 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : √3 : 2. Therefore, the formula for the ratio of the sides is c: c√3 : 2c where:
c is the shortest side opposite the 30° angle.c√3 is the side opposite the 60° angle.2c is the longest side (hypotenuse) opposite the right angle.Question 20Side x is the hypotenuse of a 45-45-90 triangle with congruent legs measuring 32 units. Therefore b = 32.
[tex]\implies x=b\sqrt{2}=32\sqrt{2}\; \sf units[/tex]
Side y is the side opposite the 60° angle in a 30-60-90 triangle with a hypotenuse of 32 units. Therefore, 2c = 32 so c = 16.
[tex]\implies y = c\sqrt{3}=16\sqrt{3}\; \sf units[/tex]
Side y is the side opposite the 30° angle in the same 30-60-90 triangle.
[tex]\implies z=c = 16\; \sf units[/tex]
Question 22Side x is the hypotenuse of a 30-60-90 triangle with the leg opposite the 30° angle measuring 7√3 units. Therefore c = 7√3.
[tex]\implies x=2c=2 \cdot 7 \sqrt{3}=14\sqrt{3}\; \sf units[/tex]
Therefore, other leg of the same triangle (opposite the 60° angle) measures c√3 = 7√3 · √3 = 21 units.
Side y is the hypotenuse of a 30-60-90 triangle with the leg opposite the 30° angle measuring 21 units. Therefore c = 21.
[tex]\implies y=2c=2 \cdot 21 = 42\; \sf units[/tex]
Side z is the leg of the same 30-60-90 triangle opposite the 60° angle.
[tex]\implies z=c\sqrt{3}=21\sqrt{3}\; \sf units[/tex]
Question 24Side z is the side opposite the 30° angle in a 30-60-90 triangle with the other leg (opposite the 60° angle) measuring 18 units. Therefore, c√3 = 18, so c = 18/√3 = 6√3 units.
[tex]\implies z=c = 6\sqrt{3}\; \sf units[/tex]
Therefore, the hypotenuse of the same triangle measures 2c = 12√3 units.
Sides x and y are the congruent legs of a 45-45-90 triangle with hypotenuse measuring 12√3 units. Therefore b√2 = 12√3, so b = 6√6.
[tex]\implies x=6 \sqrt{6}\; \sf units[/tex]
[tex]\implies y=6 \sqrt{6}\; \sf units[/tex]
Simplify:
cos^2(a) /( sin(a)-1)
[tex]\cfrac{cos^2(a)}{sin(a)-1}\implies \cfrac{1-sin^2(a)}{sin(a)-1}\implies \cfrac{\stackrel{ \textit{difference of squares} }{1^2-sin^2(a)}}{sin(a)-1} \\\\\\ \cfrac{[1-sin(a)][1+sin(a)]}{sin(a)-1}\implies \cfrac{~~\begin{matrix} [1-sin(a)] \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~[1+sin(a)]}{-[~~\begin{matrix} 1-sin(a) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~]}\implies -[1+sin(a)][/tex]
Answer:-1
Step-by-step explanation:
[tex]\frac{cos^{2}a}{sina-1} \\cos^{2}a=\frac{1+cos2a}{2}\\\frac{\frac{1+cos2a}{2}}{sina-1}=\frac{1+cos2a}{2(sina-1)}=\frac{1+cos2a}{2sina-2}=\frac{1+cos2a}{-(2-2sina)}\\1-2sina=cos2a\\\frac{1+cos2a}{-(1+(1-2sina))}=\frac{1+cos2a}{-(1+cos2a)}=-1[/tex]
If someone help I’ll be thankful!!!
Answer:
m<v = m<w
Step-by-step explanation:
I do not know how to explain it. CD are parallel with those to lines. They ahve the same degree as the other two angles.
<y = <z are opposite angle.
<w + <x = 180 are suplementary angle which mean they add up to 180.
Hei can someone help me with math homework
It would take approximately 12.5 hours for only pipe A to fill the pool, 168 hours for only pipe B, 48.6 hours for only pipe C, and 3.5 hours for all pipes.
What is equations ?
An equation is a mathematical statement that shows two expressions to be equal to each other. It typically contains one or more variables, and solving the equation involves finding the values of the variables that make the equation true. Equations are used in many areas of mathematics, science, engineering, and other fields to describe relationships between different quantities or to solve problems. Examples of equations include linear equations, quadratic equations, and differential equations.
Let's represent the amount of work done by each pipe per hour:
Pipe A: a
Pipe B: b
Pipe C: c
From the problem, we know that:
a + b = 1/9.5 (1) (pipes A and B take 9.5 hours to fill the pool)
b + c = 1/6 (2) (pipes B and C take 6 hours to fill the pool)
a + c = 1/10 (3) (pipes A and C take 10 hours to fill the pool)
We can solve this system of equations to find the values of a, b, and c:
Adding (1) and (2), we get:
a + 2b + c = 1/9.5 + 1/6
Multiplying both sides by 2, we get:
2a + 4b + 2c = 1/4.75 + 1/
Simplifying, we get:
2a + 4b + 2c = 13/28 (4)
Adding (1) and (3), we get:
2a + b + c = 1/9.5 + 1/10
Multiplying both sides by 20, we get:
40a + 20b + 20c = 2 + 1.9
Simplifying, we get:
40a + 20b + 20c = 3.9 (5)
Now we can solve for a, b, and c using (4) and (5). Multiplying (4) by 5 and subtracting (5) from it, we get:
6b = 1/28
Simplifying, we get:
b = 1/168
Substituting b into (1), we get:
a = 1/9.5 - 1/168
Simplifying, we get:
a = 1/12.32
Substituting b into (2), we get:
c = 1/6 - 1/168
Simplifying, we get:
c = 7/336
Now we can find the time it takes for each pipe to fill the pool individually:
Only pipe A: 1/a = 12.32 hours ≈ 12.5 hours
Only pipe B: 1/b = 168 hours
Only pipe C: 1/c = 48 hours ≈ 48.6 hours
All pipes: 1/(a+b+c) = 3.46 hours ≈ 3.5 hours (using the values we found for a, b, and c)
Therefore, it would take approximately 12.5 hours for only pipe A to fill the pool, 168 hours for only pipe B, 48.6 hours for only pipe C, and 3.5 hours for all pipes.
To know more about equations visit :
https://brainly.com/question/22688504
#SPJ1
Suppose we want to chose 2 objects without replacement from 3 objects how many ways can this be done with choice matter and with choice does not Matter
There are 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters and 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.
What is the factοrial?The prοduct οf all pοsitive integers less than οr equal tο a given pοsitive integer and denοted by that integer and an exclamatiοn pοint. Thus, factοrial seven is written 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factοrial zerο is defined as equal tο 1.
If the chοice matters (i.e., the οrder οf the chοsen οbjects matters), then there are 3 pοssible chοices fοr the first οbject and 2 pοssible chοices fοr the secοnd οbject.
Thus, there are 3 * 2 = 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters.
If the chοice dοes nοt matter (i.e., the οrder οf the chοsen οbjects dοes nοt matter), then there are 3 chοοse 2 = 3!/((3-2)!*2!) = 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.
Therefοre, there are 6 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice matters and 3 ways tο chοοse 2 οbjects withοut replacement frοm 3 οbjects if the chοice dοes nοt matter.
To learn more about the factorial visit:
https://brainly.com/question/25997932
#SPJ1
Can anyone help me with number 3?
Answer:
the least is 40 the greatest is 49
Step-by-step explanation:
Answer:
40 the greatest is 49
Step-by-step explanation:
I WILL GIVE 70 POINTS AND THE BRAINLIEST PLEASE HURRY!!!
Jill solves the equation: 4(x - 7) - 2x = 0
Fill in the blanks with the correct values.
4x + - 2x = 0
2x =
x =
Answer:
1) 4x -28 - 2x = 0
2) 2x = 28
3) x = 14
Step-by-step explanation:
1) 4 * (-7) = -28
2) 4x - 2x = 28
2x = 28
3) x = 28/2
x = 14