The Filling time is After 25 minutes, both Aquariums will contain same amount of water.
What is filling time?you've fully prepared the aquarium, all you need to do is follow these quick and easy steps and safely fill your aquarium with water.
Calculate the Filling Time of the aquarium Explanation
Given,
Water in Aquarium A = 4.6 gallons
Water in Aquarium B = 54.6 gallons
Filling rate = 1.2 gallons per minute.
Draining rate = 0.8 gallons per minute.
Let,
x represents the minutes.
A(x) = 4.6 + 1.2x
(Because Luis is adding water in the tank.)
B(x) = 54.6 - 0.8x
(Isacc is draining water from the tank.)
For same amount of water;
A(x) = B(x)
4.6+1.2x=54.6-0.8x
1.2x+0.8x=54.6-4.6
2x=50
Dividing both sides by 2
2x/2=50/2
x=25
Therefore, After 25 minutes, both Aquariums will contain same amount of water.
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solve for x : 4x-6=x+9
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: 4x - 6 = x + 9[/tex]
[tex]\qquad \sf \dashrightarrow \: 4x - x = 9 + 6[/tex]
[tex]\qquad \sf \dashrightarrow \: 3x = 15[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 15 \div 3[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 5[/tex]
Answer:
Step-by-step explanation:
4x-6=x+9
4x-x=9+6
3x=15
Final answer: x = 5
How do you check if an inverse is a function?
If a value of y relates only to one value of x, then the function does have an inverse function.
Define the term function and its inverse?A relation between such a collection of inputs and outputs is known as a function.
A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is just the input.If and only if the outcome of reflecting a function's graph about the line y = x is the function's graph, then the function f does have an inverse (passing from the vertical line test).Thus, if a value of y relates only to one value of x, then the function does have an inverse function.
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Angle AOB is a central angle with a measure of 110 degrees.
What is the measure of its arc AB?
The measure of the ACB arc is 250° when in the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
Given that,
In the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
We have to find the measure of the ACB arc.
We know that,
Suppose that AB is the minor arc that is m(arc AB) = 110°
We know that measure of the major arc is 360°- measure of minor arc.
m(arc ACB)= 360- m(arc AB)
m(arc ACB)= 360-110
m(arc ACB)= 250°
Therefore, The measure of the ACB arc is 250° when in the picture we have a circle with an angle AOB is a central angle with a measure of 110°.
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Reggie made a scale drawing of a house. In real life, the garage is 3 meters wide. It is 6 millimeters wide in the drawing. What is the drawing's scale factor?
Answer:
1:50
Step-by-step explanation:
The drawing's scale factor is
1:50
Explanation:
In drawing, width of the garage is 6 cm and in actual width of the garage is 3m or 3×100=300 cm.
Hence, the drawing's scale factor is 6:300 and dividing by 6, it is 1:50
How many triangles are there in the following figure 18 17 16 15?
There are 15 triangles in the given figure. Each of the four shapes in the figure can be divided into four triangles.
The figure contains four triangles, each with three sides. To calculate the total number of triangles in the figure, we can multiply the number of sides of each triangle by the number of triangles. Therefore, the total number of triangles in the figure is 3 x 4 = 12.
However, the figure also contains two additional triangles that are formed when three of the triangles intersect. To calculate the total number of triangles, we must add the two additional triangles to the 12 triangles we calculated earlier. Thus, the total number of triangles in the figure is 12 + 2 = 14.
Since the figure also has three more sides, it can be divided into one more triangle. Therefore, the total number of triangles in the figure is 14 + 1 = 15.
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What are the different types of time complexity analysis available?
There are five different types of Time complexity analysis:
Constant Time ComplexityLogarithmic Time Complexity Linear Time Complexity O(n log n) Time ComplexityQuadratic Time ComplexityWhat is Time complexity?
The computational complexity that describes the amount of computer time required to run an algorithm is known as time complexity in computer science. The time complexity of an algorithm is commonly estimated by counting the number of elementary operations performed by the algorithm, assuming that each elementary operation takes a fixed amount of time to perform.
As a result, the time required and the number of elementary operations performed by the algorithm are assumed to be proportional. Because the running time of an algorithm varies among different inputs of the same size, the worst-case time complexity, which is the maximum amount of time required for inputs of a given size, is commonly considered.
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Express 1/2 loga16 + 1/3loga27 as logab
Answer:
[tex]log_{a}[/tex] 12
Step-by-step explanation:
using the properties of logarithms
• nlog x ⇔ log[tex]x^{n}[/tex]
• log x + log y = log (xy)
[tex]\frac{1}{2}[/tex] [tex]log_{a}[/tex] 16 + [tex]\frac{1}{3}[/tex] [tex]log_{a}[/tex] 27
= [tex]log_{a}[/tex] [tex]16^{\frac{1}{2} }[/tex] + [tex]log_{a}[/tex] [tex]27^{\frac{1}{3} }[/tex]
= [tex]log_{a}[/tex] [tex]\sqrt{16}[/tex] + [tex]log_{a}[/tex] [tex]\sqrt[3]{27}[/tex]
= [tex]log_{a[/tex] 4 + [tex]log_{a}[/tex] 3
= [tex]log_{a}[/tex] (4 × 3)
= [tex]log_{a}[/tex] 12
Compare your response to the sample response above. Did your explanation include that distance is a function of time? include that the constant rate of change, or slope, is 64? include the equation y = 64x + 22? say to substitute 4 in for x to get 278 miles?
Yes the explanation satisfy the questions stated.
How to compare the value?From the question, distance is said to be a function of time and the constant rate of change is 64.
y = 64x + 22
The above is in the form of a Linear equation:
y = mx + c
Where y = dependent variable (distance)
x = unrelated variable (time)
m = slope = time/distance
22 for c = constant.
m = constant rate of change = 64
If x (time) = 4
y (distance) = 278 miles
y = 64(4) + 22
y = 256 + 22
y = 256 + 22
y = 278 miles
Therefore the value of y is 278 miles.
The complete question is : Distance is a function of time. The constant rate of change is 64. Write
the equation Y=64x + 22. Substitute 4 in for x to get 278 miles,
Compare your response to the sample response above. Did your explanation
include that distance is a function of time?
include that the constant rate of change, or slope, is 64?
include the equation y = 64x + 22?
say to substitute 4 in for x to get 278 miles?
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I don´t understand the last one
The horizontal distance that the boat is from the lighthouse is 920.31 feet
What is an equation?An equation is used to show the relationship between numbers and variables.
Trigonometric ratio shows the relationship between the sides and angles of a right angled triangle.
A beacon light is 113 feet above the water. The angle of elevation to the beacon is 7 degrees.
Let d represent the horizontal distance from the house.
Using trig ration:
tanФ = opposite/adjacent
Substituting:
tan(7) = 113 / d
d = 920.31 feet
The horizontal distance is 920.31 feet
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6) Set up and solve an equation to
find x PLEASE SHOW WORK AND ALSO TELL ANSWER I NEED HELP also it is NOT 37.5
Answer:
is not 37.5
it's 25
Step-by-step explanation:
25+25+15+115=180
50+130=180
180=180
Answer:
25°
Step-by-step explanation:
25 + x + 15 = 3x – 10 ( Sum of two opposite interior angles is equal to the exterior angle)
40 + x = 3x - 10
40 + 10 = 3x - x
50 = 2x
[tex]x = \frac{50}{2} [/tex]
x = 25°
The table shows the average speed of
the winner of a car race for different
years. About how many miles did the
winner of the car race in 2015 travel
after 2 hours? Round to the nearest
whole number.
The distance traveled after 2 hours will be 324 miles.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
The table shows the average speed of the winner of a car race for different
years.
year average speed
2005 135.17
2010 137.28
2015 161.94
2020 141.11
In order to find out how many miles the winner of the car race in 2015 traveled after 2 hours, we need to know the average speed at which they were traveling, which is given as 161.94 miles per hour. To find out how far they traveled in 2 hours, we can multiply this speed by the time, measured in hours.
So, if the average speed was 161.94 miles per hour, then the distance traveled in 2 hours is:
161.94 miles/hour × 2 hours = 323.88 miles.
Rounding up to the nearest whole number, the distance traveled after 2 hours is 324 miles.
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The question seems to be incomplete the missing table has been attached below
URGENT!!!
Which of the following points best represents the location of -1 5/8 on the number line?
A
B
C
D
Answer:
A
Step-by-step explanation:
[tex]-2<-1 \frac{5}{8}<-1[/tex], and A is the only point between -2 and -1.
Answer: i believe your answer would be C.
Step-by-step explanation: it is located where -1 is and is on the 5th line. between -1 and the letter C there are 8 lines. So answer would be letter C. sorry if that’s wrong.
What does 8 mean in math?
The number 8 (eight) is represented by a number and numeral.
It is the natural number that follows seven and precedes nine. Given that it is an integer and a cardinal number, it can be counted. It is distinguished from imaginary numbers by being categorised as a real number.
Eight is a composite number, and its proper divisors are 1, 2, and 4. Eight can be written as 23, which when said aloud sounds like two cubed. It has a 7 aliquot total. All powers of two add up to an aliquot that is one less than their own.
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What kind of line is y 2x 3?
Answer: It is a straight line
Step-by-step explanation:
Can you help me with this
The graph of the line y = 4x + 3 is shown below.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
y = 4x + 3
When x = 0, y = 3
When x = 1, y = 4 + 3 = 7
When x = 2, y = 11
Similarly for negative x values, we get,
x = -1, y = -4 + 3 = -1
x = -2, y = -8 + 3 = -5
So on......
So we must get the following coordinates:
(-1, -1), (-2, -5), (0, 3), (1, 7), (2, 11),, ........
Thus,
The graph is shown below.
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A new disease has been observed, and experts believe that 1% of the population have it. A test is developed that has 95% true positive rate (it identifies 95% of people with the disease as "positive") and 1% false positive rate (it misidenfies 1% of people without the disease as "positive"). If Alice tests positive and the experts are right on the population prevalence, what is the probability that Alice has the disease (up to 2 decimal places)?
If Alice tests positive and the experts are right on the population prevalence, the probability that Alice has the disease is 0.489.
In the given question, a new disease has been observed, and experts believe that 1% of the population have it.
A test is developed that has 95% true positive rate and 1% false positive rate.
From the given data,
Let E be the event that a patient has a disease and F be the event that a patient has tested positive.
Then according to Bayes' theorem we have,
P(E/F) = P(E)P(E/F)}/(P(E)P(E/F)+P(E')P(F/E')
P(E/F) = (1*95)/(1*95)*(99*1)
P(E/F) = 95/194
P(E/F) = 0.489 (approx.)
Hence, the probability that Alice has the disease 0.489.
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what is the probability that you get a total of 17 given You are playing a version of the roulette game, where the pockets are from 0 to 10 and even numbers are red and odd numbers are black (0 is green). You spin 3 times and add up the values you see. What is the probability that you get a total of 15 given on the first spin you spin a 2
In the roulette game, the probability that you get a total of 15 given on the first spin you spin a 2 is 8.26%
To find: the probability that you get a total of 15 in three trials
Given that you spin a 2 on the first trial.
This means, the required probability is equivalent to the probability of finding a sum of 13 in the next two trials.
In each trial, there are 11 possible outcomes as the pockets numbered from 0 to 10.
so the sample space i.e., the total number of outcomes is:
S = 11^2
S = 121
And the favourable outcomes would be,
(2, 11), (3, 10), (4, 9), (5, 8), (6, 7), (7, 6), (8, 5), (9, 4), (10, 3), (11, 2)
So, the number of favourable outcomes A = 10
Using the definition of probability,
P = A/S
P = 10/121
P = 0.0826
P = 8.26%
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The complete question is:
You are playing a version of the roulette game, wherethe pockets arefrom 0 to 10 and even numbers are red and odd numbersare black (0 isgreen). You spin 3 times and add up the values yousee. What is theprobability that you get a total of 15 given on thefirst spin youspin a 2
For a project in his Geometry class, Elijah uses a mirror on the ground to measure the height of his school building. He walks a distance of 8. 25 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. He then steps 0. 8 meters to the other side of the mirror, until he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1. 45 meters. How tall is the school? Round your answer to the nearest hundredth of a meter
The school is 24.63 meters tall.
To calculate the height of the school, Elijah can use the concept of similar triangles. Since the mirror is on the ground and parallel to it, the angle between the ground and the line from his eyes to the mirror is 90 degrees. The angle between the ground and the line from his eyes to the top of the school is also 90 degrees. The triangle formed by these lines and the line from his eyes to the top of the school is similar to the triangle formed by these lines and the line from his eyes to the mirror.
Using the similar triangles, the ratio of the height of the school to the distance from Elijah's eyes to the mirror is equal to the ratio of the distance from Elijah's eyes to the ground to the distance from the mirror to the school.
Therefore
(Height of school) / (Distance from eyes to mirror) = (Distance from eyes to ground) / (Distance from mirror to school)
Plug in the given values:
(Height of school) / 0.8 = 1.45 / (8.25 - 0.8)
Solving for the height of the school:
Height of school = (0.8 * 1.45) / (8.25 - 0.8)
= 1.16 / 7.45
= 0.1562
= 24.63 meters
The school is 24.63 meters tall.
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Plot the data in a scatter plot
A scatter plot which represents relationship between the time (in hours) and height (in meters) has been plotted in the image attached below.
How to construct and plot the data in a scatter plot?In this scenario, the time (in hours) would be plotted on the x-axis (x-coordinate) of the scatter plot while the height (in meters) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.
From the scatter plot (see attachment) which models the relationship between the time (in hours) and height (in meters), a linear equation for the line of best fit is given by
y = -0.29x + 0.52
In conclusion, we can reasonably infer and logically deduce that the scatter plot indicates an inverse relationship between the time (in hours) and height (in meters).
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What are the 11 identities?
Trigonometric identities are categorized as various identities out of which 11 are ,
Sin θ = 1/Coc θCos θ = 1/Sec θ Tan θ = 1/Cot θTan θ = Sin θ/Cos θCot θ = Cos θ/Sin θSin (90 – θ) = Cos θCos (90 – θ) = Sin θTan (90 – θ) = Cot θCot ( 90 – θ) = Tan θSec (90 – θ) = Cos θCos (90 – θ) = Sec θSin (-θ) = – Sin θTrigonometric Identities are used when trigonometric functions are given in an expression. Geometrically, these identities include one or more trigonometric functions
These are the sine , cosine or the tangent functions.
There are numerous trigonometric identities relating the side length and angle of a triangle. Only the right-angle triangle has the trigonometric identities.
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What do you call two angles whose measures have a sum of 180?
Answer:
supplementary angles
Step-by-step explanation:
for instance, 50 + 130 = 180.
it takes 4 pounds of apples to make 6 cups of apple sauce at this rate how much apple sauce can you make with 10 pounds of apples
Answer: 12 cups of applesauce
Step-by-step explanation:
A rare Pokemon trading card deck you have been wanting to buy costs 4500. You have earned 2485 from helping your mom in her online selling business. If you can save 155 weekly from your allowance, how many weeks would it take for your funds to reach 4500
Answer:
POKEMON YEAH!
Okay, so you first want to take 2485, and subtract it from 4500, because that is the amount of money he has already collected.
4500 - 2485 = 2015
Now you need to find out how many time you can multiply 155, to get 2015, or higher. In this case, I am just gonna divide:
2015/155 = 13
It will take him 13 more weeks to have enough for the Pokemon cards!
Step-by-step explanation:
Hope it helps! =D
The residents of downtown neighborhood designed a triangular-shaped park as part of a city beautification program. The park is bound by streets on all sides. The second angle of the triangle is 5 degrees more than the first. The third angle is 5 degrees less than four times the first. Find the measures of the angle
The triangular park has three angles: 60°, at its base, 55° at its top, and 65° at its base.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angle of triangle = 180
As part of a civic beautification initiative, residents in a downtown neighbourhood created a park with a triangle shape.
Let's say that the initial angle is x°.
Accordingly, the second angle is (x + 5)° and the third angle is (5x - 5)° from the information provided.
The inner angles of a triangle are known to add up to 180 degrees.
∴ x + (x + 5) + (x - 5) = 180°
3x = 180°
x = 180°/3
x =60 °.
Hence, the triangular park has three angles: The triangular park has three angles: 60°, at its base, 55° at its top, and 65° at its base.
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Circumference question
1. Suppose a bottle of Buckley's has a radius of 2cm. If you created a label for this product. What is the length of this label?
2. Assumes the company uses 22cm x 12cm boxes for delivery to stores. How many vials will be in each box?
suppose the price of each vial is $5.00. What is the cost of a box?
What is an example of an x-intercept?
An example of x-intercept is (3,0).
Here x=3 is the x-intercept in this line.
By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.
We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.
The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.
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Mr. Reginer's class has been struck with hiccups. Three of the students track their number of hiccups over time
Answer:
Step-by-step explanation:
I dont understand the question.
Unit sales for new product ABC have varied in the first seven months of this year as follows: Feb 285 Mar Apr May Jun Jul Month Jan 314 158 482 284 310 281 Unit Sales What is the (population) standard deviation of the data? Please round your answer to the nearest integer. Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel
The population standard deviation of the data is 111.
1. Find the mean of the data:
Mean = (314 + 158 + 482 + 284 + 310 + 281) / 6 = 1029 / 6 = 171.5
2. Find the difference between each data point and the mean:
Feb: (314 - 171.5) = 142.5
Mar: (158 - 171.5) = -13.5
Apr: (482 - 171.5) = 310.5
May: (284 - 171.5) = 112.5
Jun: (310 - 171.5) = 138.5
Jul: (281 - 171.5) = 109.5
3. Square each of the differences:
Feb: (142.5)^2 = 20,312.5
Mar: (-13.5)^2 = 182.25
Apr: (310.5)^2 = 95,822.25
May: (112.5)^2 = 12,656.25
Jun: (138.5)^2 = 19,082.25
Jul: (109.5)^2 = 11,982.25
4. Sum all of the squared differences:
20,312.5 + 182.25 + 95,822.25 + 12,656.25 + 19,082.25 + 11,982.25 = 149,047.5
5. Divide the sum of the squared differences by the number of data points minus one:
149,047.5 / (6 - 1) = 149,047.5 / 5 = 29,809.5
Square root of 29,809.5 = 111 (rounded to the nearest integer)
Therefore, the population standard deviation of the data is 111.
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What is the degree of the polynomial 2x² 3xy 5y² 2?
The degree of the given polynomial is 2 because the highest exponent is 2 present in terms 2x^2 or 5y^2.
First, try to understand what is polynomial.
Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. x^2+ 3x - 5 is an illustration of a polynomial with a single variable. There are three terms in this example: x^2, 3x, and -5.
The word "polynomial" is derived from the Greek words "poly" and "nominal," which combined translate to "many phrases."
Now let's talk about the degree of the polynomial.
The highest exponent of a monomial contained within a polynomial is referred to as the polynomial's degree. As a result, a polynomial equation with one variable having the biggest exponent is referred to as a polynomial degree.
The terms of a given polynomial is 2x^2, 3xy, 5y^2, and 2 Highest exponent is 2 in 2x^2 or 5y^2.
So the degree of the polynomial is 2.
The given Question is an incomplete complete question here.
[tex]2x^2 + 3xy + 5y^2 +2[/tex].
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Explain why the initial value of any function of the form
f(x)= a(b) is equal to a.
Hello there!
Initial value is the y-intercept so x = 0. Then b⁰ = 1 because x⁰ = 1 if x ≠ 0. So the value of function is a * 1 which is equal to a.
Step-by-step explanation: The initial value of any function of the form f(x)= a(b) is equal to a because this type of function is a linear equation, which means that the rate of change (slope) is constant. This means that the output is always equal to the input multiplied by a constant, which is the coefficient a. Therefore, when the input (x) is equal to 0, the output (f(x)) is equal to 0 multiplied by a, which is equal to a.