Answer:
To solve this problem, we need to use the formula for the volume of a cylinder: V = πr^2h, where V is the volume, r is the radius, and h is the height.
Step 1: We know that the radius of the tank is 2 feet and that it is being filled at a rate of 4 cubic feet per minute. We also know that the tank is half full, so we can assume that the height of the water in the tank is half the height of the tank itself.
Step 2: We can use the volume formula to find the volume of the tank when it is half full.
V = πr^2h
V = π(2^2)(h/2)
V = 4πh/2
Step 3: We can divide the rate of fill by the volume of the tank when it is half full to find the rate of change of the height of the water.
dh/dt = 4/(4π/2)
dh/dt = 2/π ft/min
Final Answer: The level of the water in the tank is rising at a rate of 2/π feet per minute when the tank is half full.
Mario is cooking dinner for his family recipe he is using calls for 2 3/4 cups of chicken broth and he only has one 1 1/3 cups how much more chicken broth does Mario need for his recipe
Answer:
1 5/12 (One whole number five over twelve)
Step-by-step explanation:
Recipe calls for 2 3/4 cups
No of cups available are 1 1/3 cups
To get the number of cups needed to fulfill the recipe well say:
1 1/3 + X = 2 3/4
X = 2 3/4 - 1 1/3 = 1 5/12
Using P.M.I , prove that 6^n - 1 is divisible by 5.
Therefore , the solution of the given problem of PMI comes out to be
6 ⁿ -1 is always divisible by 5.
What is the purpose of mathematical induction?A mathematical method known as mathematical induction is used to demonstrate that a claim, formula, or theorem holds true for every natural number. Step 1 (Base Step) demonstrates the truth of a statement for the starting value.
Here,
Given : 6 ⁿ -1 is divisible by 5
Let,
=> 6 ⁿ -1
=> 6 ¹ - 1
=>5
P(k) is divisible by 5
P(k+1)=6
k+1−1=6.6k−1
=(5+1).6k−1
=5×6 k+6k−1
=5×6k+5m
=5(6k+m)
P(k+1) is divisible by 5
Therefore , the solution of the given problem of PMI comes out to be
6 ⁿ -1 is always divisible by 5.
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if a regression model is estimated using observations on each of these variables, what are the degrees of freedom (df) for the regression sum of squares, error sum of squares, and total sum of squares?
The degrees of freedom for the regression sum of squares in a regression model is determined by the number of variables that are being used to make predictions. For example, if you have three independent variables in your model, the degrees of freedom for the regression sum of squares would be 3.
The degrees of freedom for the error sum of squares is the total number of observations in your dataset, minus the number of independent variables used in the model.
The total sum of squares is the sum of the squared differences between each observation and the overall mean of the variable being predicted. This has the same number of degree of freedom as the error sum of squares, which is total number of observations -1.
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In Exercises 1-4, find the exact values of the six trigono-
metric functions of the angle shown in the figure. (Use the
Pythagorean Theorem to find the third side of the triangle.)
1.
2.
0
8
6
0
13
5
Only number 1 and 2
Answer:
1. 10
2. 12
Step-by-step explanation:
1. 8² + 6² = y² (Taking the unknown side as y)
64 + 36 = 100
y² = 100
y = 10
2. 5² + x² = 13² (Taking the unknown side as x)
x² = 13² - 5²
= 169 - 25
= 144
x² = 144
x = 12
1. An angle is in standard position such that sin Ø-5/9. What are the possible values of Ø, to the nearest degree if 0 ≤0360? State the larger of
the two angles.
The larger possible angle of sin Ф = (5/9) is 34°.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
sin Ф = 5/9
Ф = [tex]sin^{-1}[/tex] (5/9)
Ф = 33.75
This means,
Ф =33° or 34°
Thus,
The larger angle is 34°.
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Find the 97th term of the arithmetic sequence -5, -23, -41, ...
Someone please help me as fast as you can!!
I would really appreciate it!
-2(3n+6) = 3(-n+12)
Solve for n
Answer:
-16
Step-by-step explanation:
find the gradient vector field of f. f(x, y) = xe^(3xy)
The gradient vector field of function f(x,y) is given as follows:
grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.
How to obtain the gradient vector field of a function?Suppose that we have a function defined as follows:
f(x,y).
The gradient function is defined considering the partial derivatives of function f(x,y), as follows:
grad(f(x,y)) = fx(x,y) i + fy(x,y) j.
In which:
fx(x,y) is the partial derivative of f relative to variable x.
fy(x,y) is the partial derivative of f relative to variable y.
The function in this problem is defined as follows:
f(x,y) = xe^(3xy).
Applying the product rule, the partial derivative relative to x is given as follows:
fx(x,y) = e^(3xy) + 3xye^(3xy) = (1 + 3xy)e^(3xy).
Applying the chain rule, the partial derivative relative to y is given as follows:
fy(x,y) = 3x²e^(3xy).
Hence the gradient vector field of the function is defined as follows:
grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.
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a researcher is interested in the relationship between caffeine consumption and activity level for elementary school children. a sample of 20 children is obtained and each child is interviewed to determine a level of caffeine consumption. the researcher then records the level of activity for each child during a 30-minute session on the playground. is this an experimental or correlational study? explain your answer.
This is an experimental study, as the researcher is manipulating the independent variable (caffeine consumption) to measure the dependent variable (activity level) in a controlled environment.
This is an experimental study, as the researcher is manipulating the independent variable (caffeine consumption) to measure the dependent variable (activity level) in a controlled environment. In an experimental study, the researcher has control over the independent variable and is able to measure the results of the manipulation on the dependent variable. In this study, the researcher is measuring the activity level of the children based on their caffeine consumption, which the researcher can control. The researcher is also measuring the activity level in a controlled environment, the playground, which provides a consistent setting for the experiment. This type of study is designed to test the researcher's hypothesis and determine whether there is a relationship between caffeine consumption and activity level.
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The velocity of a drone, during the first minute of flying, is recorded in the table below. Time (seconds) 0 10 20 30 40 50 60 Velocity (ft./sec) 20 22 26 30 36 34 32Using the left-hand rectangular approximation method (LRAM), what is the approximate total distance the drone flies during the first minutea. 1.480 ftb. 1.680 ftc. 1.800 ftd. 4.780 ft
Answer: 1680 ft
Step-by-step explanation:
See attachment
An airplane is preparing to land at an airport. It is 45,600 feet above the ground and is descending at the rate of 3,200 feet per minute. At the same airport, another airplane is taking off and will ascend at the rate of 2,500 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be?
Answer:
8 mins 20000feet
Step-by-step explanation:
let mins be x
45600-3200x = 2500x
so 45600= 5700
x=8
2500*8 = 20000
ange the following polynomial in column and then add 1.(9x+3y)+(5x-4y)
)????????????????????????????????????????????????
Answer:
14x - y
Steps:
(9x + 3y) + (5x - 4y)
Determine the sign:
9x + 3y + 5x - 4y
Combine as terms:
14x - y
I hope it helps you :)
State if the polygons are similar
Answer:
Yes, they are similar by SSS
Work out the bearing d from a
Answer:
Below in bold.
Step-by-step explanation:
m < DAC = 360 -15 - 155 - 166
= 24⁰
The bearing of D from A
= 180 + 15 + 24
= 219⁰
or S 39⁰ W.
Think About the Process At a supermarket, a 6-ounce bottle of brand A salad dressing costs $1.56. A 14-ounce bottle costs $3.36. A 20-ounce bottle costs $5.60. What unit prices do you need to know to find the best buy? What is the best buy?
a) The unit prices to determine the best buy are as follows:
6-ounce bottle = $0.2614-ounce bottle = $0.2420-ounce bottle = $0.28.b) The best buy is the 14-ounce bottle of salad dressing with a unit cost of $0.24 since they are all Grade A products.
What is the unit price?The unit price or cost is the cost for an item or a unit.
The unit price can be compared to the unit rate, which is the quotient of the total cost and the number of units.
6 ounces 14 ounces 20 ounces
Total costs $1.56 $3.36 $5.60
Unit cost $0.26 $0.24 $0.28
($1.56/6) ($3.36/14) ($5.60/20)
Thus, buying a 14-ounce bottle of salad dressing is more economical than others.
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Which value could be substituted for the variable to make the equation TRUE? 24 = 4y
hello! please help me find the x & y intercepts, domain & range, relative minimum & maximum, increasing & decreasing intervals, and positive & negative intervals.. thank you :)
Solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain.
How do you find the domain and range of X and Y?We can easily identify the values of the independent variable x and the domain by solving the equation y = f(x). The range may then be found by solving for x.
For a relation, the domain and range are defined as sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively. For instance, if the relationship is R = (1, 2), (2, 2), (3, 3), and (4, 3), then
The collection of all x-coordinates with values 1, 2, 3, and 4 is known as the domain.Range is the set of all y-coordinates with values of 2, 3.
The elements that make up a function are its domain and range. A function's domain is the set of all potential input values, while its range is the range of possible output values. Range, Function, and Domain.
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What is the distance formula for a triangle?
The distance formula for a triangle is the Pythagorean Theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The distance formula for a triangle is the Pythagorean Theorem, which outlines a relationship between the three sides of a right triangle. Specifically, the theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. To find the distance between two points in a triangle, you must first determine the length of all three sides. Once you know the lengths of all three sides, you can use the Pythagorean Theorem to calculate the distance between the two points. To use the theorem, you must first calculate the square of the hypotenuse. Then, you must square the lengths of the other two sides and add them together. Finally, you can take the square root of the sum of the squares to calculate the distance between the two points.
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Supplementary angles are two angles that have measures with a sum of 180°. Angles 1 and 2 are supplementary and the measure of angle 2 is 3° more than twice the measure of angle 1.
Write a system of equations and use substitution to find the measures of angles 1 and 2.
100 characters remaining
Answer:
Step-by-step explanation:
180 total
180-3=177
ratio of angle 1 to angle 2:
2:1
we need to divide 177 by 3 since there are 3 parts in the ratio above
177/3=59
angle 1 = 59x2=118
angle 1=118 degrees
angle 2=59+3=62
angle 2 =62 degrees
we can check by adding 62 and 118
62+118=180
plsssssshelppppppppppp
Answer:
1
Step-by-step explanation:
What is the area of the figure at the right?
(It's not H)
Answer:
96m2
Step-by-step explanation:
First we have to find the perimeter of parallelogram
Now,
Breadth(b)=10m
Height(h)=6m
Perimeter of paralleogram(p)=b×h
=10×6
=60m
Then,
Breadth(b)=12m
Height(h)=6m
Perimeter of triangle(p)=1×b×h
2
= 1 ×6×12
2
=36m2
Now,
Perimeter of above figure= Perimeter of paralleogram+perimeter of triangle
= 60+36
. =96m2
liam sells sandwiches at an arena. he earns $10.50 per hour plus $0.40 for each sandwich he sells. how many sandwiches does he need to sell during a 6-hour shift to earn $125
Answer:
He needs to sell 157 sandwiches to earn $125
Step-by-step explanation:
●$10.50×6 hrs= $63
●$125 - $63= $62 {So he needs to sell $62 worth of sandwiches}
●$0.40 × 157= $62
pov:《$62 + $63 = $125》
Answer:
155 sandwiches
Step-by-step explanation:
First we see what the base rate is for his six-hour shift. We do this by multiplying 10.50 by 6 which is 63. Then we do 125-63 which is 62. As he gets 42 cents per sandwich so we do 62÷0.40, which equals 155 so he needs to sell 155 sandwiches.
which compact sets does there exist a number m such taht every open cover contains a finite subcover of m elemens
The unit interval [0,1] in the real numbers is a compact set, and we can find a number m such that every open cover of [0,1] contains a finite subcover of m elements.
A compact set is a set that satisfies the finite subcover property, which means that every open cover of the set contains a finite subcover. This means that for any open cover of a compact set, there exists a finite subcover containing a certain number of elements (m) that can cover the entire set.
Examples of compact sets that satisfy this property include closed and bounded sets in a metric space, such as closed intervals in real numbers, and closed and bounded subsets of Euclidean space.
The unit interval [0,1] in the real numbers is a compact set, and we can find a number m such that every open cover of [0,1] contains a finite subcover of m elements.
Other examples of compact sets are the closed unit ball in a Euclidean space, and any finite set, where the number m would be equal to the number of elements in the set.
In summary, compact sets are sets that have the property of finite subcover, and for any open cover of a compact set, there exists a finite subcover containing a certain number of elements (m) that can cover the entire set. Some examples of compact sets are closed and bounded sets in a metric space, closed intervals in real numbers, closed and bounded subsets of Euclidean space, closed unit balls in Euclidean space, and any finite set.
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what is the common ratio of the geometric system 24,6,1.5,0.75
Answer:
0.25 or 1/4
Step-by-step explanation:
To find the common ration in a geometric sequence, divide the second number by the first number. In this case, divide 6 by 24.
P. S. If you find my answer the most helpful could you please choose it as the Brainliest? Have a great night!
(01.02 MC)
Determine the solutions of the equation:
|1/3×+9|-3=21
Ox= -11 and x = 5
Ox= -81 and x = 45
O x = -99 and x = 45
O x = -99 and x = 99
The solution for given linear equation are x=-99 and x=45 i.e. C.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
Given linear equation is |1/3×+9|-3=21
so, -1/3x-12=21 --->1
and 1/3x+6=21 --> 2
From 1
1/3x=-33
x=-99
From 2
1/3x=15
x=45
Hence,
The solution for given linear equation are x=-99 and x=45.
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Help me please thank you
Answer: 20 + x = y.
Step-by-step explanation:
When you deposit, you are adding onto something. Because there is no real value for x, the expression would be 20 + x = y. Also, it would be = y because it says clearly the total amount would be equal to y. and also since why has no value in this context, it would still be y.
An experienced bricklayer can work twice as fast as an apprentice bricklayer. after the bricklayers work together on a job for 4 hours, the experienced bricklayer quits. the apprentice requires 14 more hours to finish the job. how long would it take the experienced bricklayer, working alone, to do the job?
The total time taken by the experienced bricklayer to complete the job as per given condition is equal to 13 hours.
As given in the question,
Let the time taken by experienced bricklayer be 't' hours
Then time taken by apprentice bricklayer be '2t' hours
Time to complete 1 complete work is
Experienced bricklayer worked for 4 hours
Apprentice bricklayer worked for ( 4 + 14 ) = 18 hours
Required equation to complete 1 work is :
( 4/x) + ( 18 /2x) = 1
⇒( 8 + 18 )/ 2x = 1
⇒26/2 = x
⇒ x = 13 hours
Therefore, time taken by the experienced bricklayer to complete the job is equal to 13 hours.
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how were subjects selected (or not selected) for the study? what (if any) impact did that process have?
So, on solving the provided question we can say that the probability P(study) = 1/1-a
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
here,
subjects selected = a
not selected = 1-a
P(study) = 1/1-a
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X, Y and Z form the vertices of a triangle, where
∠
YXZ = 57°,
∠
YZX = 47°, and XZ = 7.2cm.
Calculate the length of YZ rounded to 1 DP
Answer:
Step-by-step explanation:
