The radius of the snowball decreasing by -2.
What is rate?
A rate is the ratio of two related values expressed in various units. [1] If one of these numbers is used as the ratio's denominator and it is assumed that this quantity can be altered in a predictable way (i.e., is an independent variable), then the numerator of the ratio represents the rate of change in the other (dependent) variable.
Let r(t) be a function of the radius of the sphere over time.
The volume of the sphere over time is then [tex]v(t) = \frac{4}{3} \pi r(t)^3[/tex]
The rate of change of the volume is then [tex]v'(t) = 4\pi r(t)^2r'(t)[/tex]
Comparing is to the surface area of the sphere [tex]s(t) = 4\pi r(t)^2[/tex], it seems perfectly possible for the volume to decrease at a rate equal to 2s(t).
That just means that
[tex]v'(t) = -2s(t)\\4\pi r(t)^2r'(t) = -8\pi r(t)^2\\r'(t) = -2[/tex]
Therefore, the radius must shrink by two units of distance every unit of time, it is now obvious.
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If Fx) = x-5 and G(x) = x2 , what is G(F(x))?
Explanation:
Given the functions
f(x) = x-5
G(x) = x^2
We are to find the composite function G(f(x))
as long as you are working with the same variables, it does not matter whether or not you average the data over every month versus every year; the correlation will be the same. group of answer choices true false
The given statement is true.
What is variables?
In statistical modelling, experimental sciences, and mathematical modelling, there are dependent and independent variables. Dependent variables are so named because they are researched in an experiment under the assumption or requirement that they are dependent on the values of other variables according to some rule or law.
The given statement is true.
It does not matter whether we average the data across every month or every year as long as the variables are the same; the correlation will remain the same. Since the correlation coefficient r is a unitless metric, the time variable has no effect on it.
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Find the equation of a line that passes through (3,-1) and is perpendicular to the equation 3x+y=2
Answer:
y = (1/3)x - 2
Explanation:
First, we need to identify the slope of the equation 3x + y = 2, so we need to solve for x as:
[tex]\begin{gathered} 3x+y=2 \\ y=2-3x \end{gathered}[/tex]Now, the number beside the variable x is the slope, so the slope is -3
Then, two lines are perpendicular if the product of both slopes is equal to -1. It means that the slope m for our equation should be:
[tex]\begin{gathered} -3\cdot m=-1 \\ m=\frac{-1}{-3}=\frac{1}{3} \end{gathered}[/tex]Now, we can find the equation of the line using the following:
[tex]y=m(x-x_1)+y_1[/tex]Where m is the slope and (x1, y1) is a point on the line. So, replacing my 1/3 and (x1, y1) by (3, -1), we get:
[tex]\begin{gathered} y=\frac{1}{3}(x-3)+(-1) \\ y=\frac{1}{3}x-\frac{1}{3}\cdot3-1 \\ y=\frac{1}{3}x-1-1 \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]Therefore, the equation of the line is: y = (1/3)x - 2
Find 3 ratios that are equivalent to 5:13
Pls pls helpp due today!
The perpendicular linear equation that passes through (8, 2) is:
y = x - 6
How to find the perpendicular line?A general linear equation is of the form:
y = m*x + b
Where m is the slope.
Two lines are perpendicular only if the product between the slopes is equal to -1.
Here we start with the line:
y = -x
So the slope is -1.
Then the slope of the perpendicular line m must be:
-1*m = -1
m = -1/-1 = 1
Then the perpendicular line is something like:
y = x + b
And we want this to pass through (8, 2), replacing these values we get:
2 = 8 + b
2 - 8 = b
-6 =b
The linear equation is:
y = x - 6
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What is the image point of (-7,3) after the transformation rx-axis o R180º?
In a composite transformation as given you make first the transformation in the right and then the transformation in the left.
For the given point: (-7, 3)
1. Rotation 180°
[tex]\begin{gathered} P(x,y)\rightarrow P^{\prime}(-x,-y) \\ \\ P(-7,3)\rightarrow P^{\prime}(7,-3) \end{gathered}[/tex]2. Reflection over x-axis:
[tex]\begin{gathered} P^{\prime}(x,y)\rightarrow P^{\prime}^{\prime}(x,-y) \\ \\ P^{\prime}(7,-3)\rightarrow P^{\doubleprime}(7,3) \end{gathered}[/tex]Then, the image of given point after the composite transformation is (7,3)You are going to drive to another state for a vacation. One route will take 8 hours to drive 400 miles, and the other route will take 7 hours to drive 420 miles. You write two equations to try and figure out the average rate of speed you would travel on each route. How much higher will your average speed be on the faster route?(1 point)
Responses
20 mph
10 mph
60 mph
50 mph
Which postulate would prove the triangles congruent?
Answer:
AAS
Step-by-step explanation:
Because of vertical angle theorem, angle rts and vtu are congruent. This means there are 2 congruent angles with a non-included side
Subtract and simplify:
PLEASE HELP ASAP
5 1/3 − 4 5/6 = _____
Responses
A 1 2/3
B 1 4/6
C 1/2
D 3/6
Answer:
C. 1/2
Hope this helps!
[tex]\boxed{\boldsymbol{\sf{5\frac{1}{3}\times4\frac{5}{6} }}}[/tex]
Multiply 5 and 3 to get 15.
[tex]\boxed{\boldsymbol{\sf{\dfrac{15+1}{3}-\left(\frac{4\times6+5}{6}\right) }}}\boldsymbol{\longmapsto \ Add \ [15+1]}[/tex]
[tex]\boxed{\boldsymbol{\sf{\dfrac{16}{3}-\left(\frac{4\times6+5}{6}\right) }}}\boldsymbol{\longmapsto \ Multiply \ [4*6+5]}[/tex]
[tex]\boxed{\boldsymbol{\sf{\dfrac{16}{3}-\left(\frac{29}{6}\right) }}}[/tex]
Convert fractions prior to fractions with equal denominators.
[tex]\boxed{\boldsymbol{\sf{\frac{32}{6}-\dfrac{29}{6}=\frac{32-29}{6}=\frac{3}{6}=\dfrac{3\div3}{6\div3}=\frac{1}{2} }}}[/tex]
The answer is 1/2, therefore the alternative is correct is option C.To eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?
First equation:
Second equation:
The first equation should be multiplied by 3 and the second equation by -5.
The first equation should be multiplied by 3 and the second equation by 5.
The first equation should be multiplied by 7 and the second equation by -6.
The first equation should be multiplied by 7 and the second equation by 6.
Answer: the answer is c)The first equation should be multiplied by 7 and the second equation by -6.
Step-by-step explanation:edge 2022
Answer:
C
Step-by-step explanation: -6
Simplify -1(15+4 - 27) over 16
[tex] \frac{ - 1(15 + 4 - 27)}{16} \\ = \frac{ - 1(19- 27)}{16} \\ = \frac{ - 1( - 8)}{16} \\ = \frac{8}{16} \\ = 0.5[/tex]
ATTACHED IS THE SOLUTION
Answer:
= - 19 + 16^27
SHOW YOUR WORK
2 x 1/4 =
Answer:
2 times 1/4 = 1/2 or 0.5
Step-by-step explanation:
Step 1: Setup
First of all, note that 2 is the same as 2/1 since 2 divided by 1 is 2. Therefore, start by setting up the problem like this:
2/1 x 1/4
Step 2: Multiply
Multiply the numerators together (2 x 1 = 2) and multiply the denominators together (1 x 4 = 4) and make it into one fraction like so:
2/4
Step 3: Minimize
The greatest common factor of 2 and 4 is 2. Minimize the fraction by dividing the numerator and the denominator by its greatest common factor to get the answer as follows:
1/2
If 8,x,y ,-4 are in A.p find x and y
Answer:
Step-by-step explanation:
firstly, 8+d=x and y+d= -4 where d is the common difference of the AP.
Also,
x+d=y;
therefore d=y-x;
so,
8+y-x=x (from the first equation)
=>8+y=2x
=>y=2x-8
Now from the second equation,
y+d= -4
(2x-8)+(y-x)= -4
=>x-8+2x-8= -4
=>3x=12
=>x=4
similarly,
y=2(4)-8
=>y=0
a scientist runs an experiment involving a culture of bacteria. she notices that the mass of the bacteria in the culture increases exponentially with the mass increasing by 229% per week. what is the 1-week growth factor for the mass of the bacteria? what is the 1-day growth factor for the mass of the bacteria? by what percent does the mass of bacteria increase by each day? % if the mass of the bacteria instead increased by 453% per week, by what percent would the mass increase by
The 1-week growth factor for the mass of the bacteria is 3.29.
The 1-day growth factor for the mass of the bacteria is 1.185.
The percentage increase in the mass of bacteria is 18.5%.
The 1-day growth percent for the mass of the bacteria if the mass of the bacteria increased by 453% per week is 27.7%.
The 1-week growth factor for the mass of the bacteria is 1 + (229%*1).
The 1-week growth factor for the mass of the bacteria is 3.29.
The 1-day growth factor for the mass of the bacteria is (3.29)^(1/7).
The 1-day growth factor for the mass of the bacteria is 1.185.
The percentage increase in the mass of bacteria is 18.5%.
The new 1-week growth factor for the mass of the bacteria is 1 + (453%*1).
The new 1-week growth factor for the mass of the bacteria is 5.53.
The 1-day growth factor for the mass of the bacteria if the mass of the bacteria increased by 453% per week is (5.53)^(1/7).
The 1-day growth factor for the mass of the bacteria if the mass of the bacteria increased by 453% per week is 1.277.
The 1-day growth percent for the mass of the bacteria if the mass of the bacteria increased by 453% per week is 27.7%.
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This is a financial mathematics problem that I need help with
SOLUTION
Carrie's credit card was stolen, she was charged $ 2,000
Hence carrier's is responsible for paying $2,000
The width of a rectangle is 3 units less than the length. The area of the rectangle is 18
units. What is the length, in units, of the rectangle?
Answer:
First let the length be a variable (eg: x) so that we can form an expression and solve.
Let the length of the rectangle be x units.
Form an expression for the width of the rectangle using the information given.
Width = (x - 3) units
Area of rectangle = length x width
Using the formula, form an equation.
x(x - 3) = 18
Simplify and solve for x.
x² - 3x = 18
x² - 3x - 18 = 0
(x - 6)(x + 3) = 0
x - 6 = 0 or x + 3 = 0
x = 6 or x = - 3 (reject)
The length cannot have a negative value so reject - 3.
Hence, the length of the rectangle is 6 units.
The log flume ride lasts 8 minutes. This amount of time is one minute more than twice the length of time for the teacup ride.
How long does the teacup ride last?
The time for the teacup to last is D. m = 3.5 minutes.
What is an expression?An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of minutes be m.
The amount of time is one minute more than twice the length of time for the teacup ride. This will be:
= (2 × m ) + 1 = 8
2m - 1 = 8
Collect like terms
2m = 8 - 1
2m = 7
Divide
m = 7/2
m = 3.5
The correct option is D.
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Answer:
d) m = 3.5 minutes
Step-by-step explanation:
Now we have to,
→ find the time the teacup ride last.
Forming the equation,
→ 2m + 1 = 8
Then the value of m will be,
→ 2m + 1 = 8
→ 2m = 8 - 1
→ m = 7/2
→ [ m = 3.5 min ]
Hence, ride lasts for 3.5 min.
24PS-10 Question Help In a certain chemical, the ratio of zinc to copper is 3 to 14. A jar of the chemical contains 294 grams of copper. How many grams of zinc does it contain?
the ratio of zinc to copper is 3 to 14, that menas that for each 3 grams of zinc there are 14 grams of copper, so we can made a rule of three to find
Solve system of equation by substitution
7y=-2x+5
3x+10y=6
Answer:
x= -8/41
y= 27/41
Step-by-step explanation:
7y=2x+5
3x+10y=6
maybe divide all parts of first equation by 7 to leave y by itself: y=2/7x+5/7
Then plug that in for y in the second equation:
3x+10(2/7x+5/7)=6
Then just solve for x:
x= -8/41
Substitute value of x into first equation:
7y=2(-8/41)+5
Solve for y:
y=27/41
In systems of equations, the values of x and y are -8 and 3, respectively.
Given systems of equations are:
7y=-2x+5 .....(i)
3x+10y=6 .....(ii)
We want both equations to be in standard form (Ax + By = C) so we need to fix the first equation.
For the equation (i), simply add 2x from both sides, so that x & y are on the same side of the equal sign
2x + 7y = 5 .....(i)
3x + 10y = 6 .....(ii)
To get the same x value in both equations (i) and (ii), we must now multiply equation (i) by 3 and equation (ii) by 2.
3(2x + 7y = 5) .....(i)
2(3x + 10y = 6) .....(ii)
Simplify.
6x + 21y = 15 .....(i)
6x + 20y = 12 .....(ii)
Now, subtract equations (ii) from (i)
y = 3
Now, substitute value of y = 3 in equation (i).
2x + 7y = 5 .....(i)
2x + 7(3) = 5
2x + 21 = 5
Then, subtract 21 from both sides.
2x + 21 - 21 = 5 - 21
2x = - 16
Divide both sides by 2.
2x / 2 = - 16 / 2
x = -8
So, x = -8 & y = 3
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p = q - r + s. solve for q
Answer:
if you can't read my pic the answer is: p+r-s=q
Step-by-step explanation:
rotate the figure 90 degrees clockwise around the origin?indentify the coordinates of the vertices of the rotated figure?
first write the coordinates
A (5,8)
B(9,8)
C(9,5)
D(5,5)
to rotate 90 degrees clockwise you must swap coordinates I mean change x for y and change the sign of the secon term or the new y
A(5,8)-->A'(8,-5)
B(9,8)-->B'(8,-9)
C(9,5)-->C'(5,-9)
D(5,5)-->D'(5,-5)
Which postulate proves the two triangles congruent?
A. SSS
B. SAS
C. ASA
D. AAS
Answer:
A. SSS
Step-by-step explanation:
Triangle ADT and triangle TDE are congruent triangles by SSS postulate.
Sides DE and DA, sides TE and TA are congruent (DT is common side).
So the answer is A. SSS
ANYONE WHO ANSWERS ILL GIVE BRAINLIEST TO
finding the slope
Answer:
slope = 50
Step-by-step explanation:
Equation of slope of line is
y = mx + b
where m = slope and b = y-intercept which is the y-value for the point at which the line crosses the y-axis
In the graph you can see that the line crosses at (0,0)
So y-intercept is 0
Equation is y = mx
To find m
take two points on the line and calculate rise/run
rise = difference in y-values
run = difference in x-values
Points(0,0) and 1, 50) lie on the line
rise = 50 - 0 = 50
run = 1-0 = 1
slope = 50 /1 = 50
the interest rate on a five-year certificate of deposit (cd) for banks in south florida in 2018 was normally distributed with a mean of 2.28 percent and a standard deviation of 0.37 percent. if a bank has an interest rate at the 45th percentile, what is the interest rate at this bank?
The interest rate at the bank = 2.324 %
Let X be the random variable representing the interest rate on a five-year certificate of deposit (cd) for banks in South Florida in 2018.
Then X follows the Normal Distribution with,
Mean, μ = 2.28 % and,
Standard Deviation, σ = 0.37 %
We need to find the X at the 45th percentile.
45th percentile implies z-value = 0.45
The z-score at 45th percentile or 0.45 probability = -0.12 [From the z-tables]
We have, z = (x-μ)/σ
⇒ zσ = x-μ
⇒ x = zσ+μ
⇒ x = (0.12 x 0.37) + 2.28
= 2.324
Hence the interest rate at the bank = 2.324 %
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The instructions on a jar of instant coffee say to add 5 cups of water to every 4 tablespoons of coffee granules. How many cups of water are needed for 10 tablespoons of coffee granules?
Answer:
12.5 cups
Step-by-step explanation:
10/4 = 2.5
2.5 × 5 = 12.5
12.5 cups
You will have $ in 15 years if you set aside $100 a year at 6%.
The most appropriate choice for simple interest will be given by -
Amount obtained = $28.5
What is simple interest?
Simple interest is the interest earned on a certain principal at a certain rate over a certain period of time.
If principal is p, rate is r%, time is t years
Simple interest = [tex]\frac{p \times r \times t}{100}[/tex]
On adding principal and simple interest, we get amount.
Amount = Principal + Simple interest.
Principal = $15
Rate = 6%
Time = 15 years
Simple interest = [tex]\frac{15 \times 6 \times 15}{100}[/tex]
= $13.5
Amount obtained = $(15 + 13.5)
= $28.5
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the time to failure of a television tube is estimated to be exponentially distributed with a rate of 3 per year. a company offers insurance on these tubes for the first year of usage. on what percentage of policies will they have to pay a claim?
On 4.98% of the policies, they will not have to pay a claim.
The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur. What are the chances of receiving a head, for instance, when we toss a coin in the air? The number of outcomes that could occur is the basis for the response to this question. The outcome in this case might be either head or tail. Therefore, there is a 50% chance that the result will be 1 / 2 head.
λ = 3 per year
To avoid having to pay a claim for these tubes, we need to determine the likelihood that they will live longer than a year.
Given by: The likelihood of tubes lasting longer than a year is
P(x > 1) = e^-λ*x
P(x > 1) = e³*¹ = 0.04978
Therefore, they won't be required to pay a claim on 4.98% of the policies.
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PLEASE HELP ASAPPPPP!!!!!!!!!!!!!
The quadratic function f(x) has roots of −2 and 6, and it passes through the point (1, 15). What is the vertex form of the equation of f(x)?
f(x) = (x − 2)2 + 16
f(x) = (x + 2)2 + 16
f(x) = −(x − 2)2 + 16
f(x) = −(x + 2)2 + 16
Answer:
f(x) = −(x − 2)^2 + 16
Step-by-step explanation:
See attached graph.
Which set of ordered pairs is a
function?
A. (-2,4), (0, 4), (2, 4), (2,6)}
B. {(-10, 4), (-8, 3), (-8, 2), (-4,1))
C. {(1, 5), (1, 6), (2,7), (3, 8))
D. Of(-1, 1), (0, 0), (1, 1), (2, 2))
A set of ordered pairs that contain only unique ordered pairs with unique x coordinates exists directed to as a function.
The set of ordered pairs is a function exists {(1, 5), (1, 6), (2,7), (3, 8)}.
What is meant by function?A set of ordered pairs that contain only unique ordered pairs with unique x coordinates exists directed to as a function. A function is defined by an equation that generates a set of ordered pairs. Each x value in a relation must have a unique value for the y value for it to be a function. if there are multiple y-values associated with an x-value.
Because no two ordered pairs have the same first coordinates with the same second coordinates, the initial set of ordered pairs is a function.
A relationship and a function vary in that a relationship can have multiple outputs for a single input, whereas a function only needs one input to produce one outcome. This is the fundamental criterion used to distinguish between relation and function. These model concepts are created through the usage of relations.
Therefore, the correct answer is option C. {(1, 5), (1, 6), (2,7), (3, 8)}.
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5Eleri has this information about holiday activities.Activity SurfingTime 1 hourCost £38Activity Horse ridingTime 4 hoursCost £45Activity ClimbingTime 3 hoursCost £40Eleri wants to show this information in a table.Organise the information in a table.(1)
Organise the information in a table.