The average rate of change when x increases from -3 to 5 is given as follows:
r = (f(5) - f(-3))/8.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the average rate of change is given by the fraction presented as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
In the context of this problem, the input x increases by -3 to 5, hence the change in the input is given as follows:
b - a = 5 - (-3) = 5 + 3 = 8.
The change in the output is given as follows:
f(b) - f(a).
(the problem is incomplete hence the answer is given in general terms).
Then the average rate of change of the function when x increases from -3 to 5 is given as follows:
r = (f(5) - f(-3))/8.
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(6x10^2)/(3x10^-5) standard form
Answer:
2×10^7
Step-by-step explanation:
cuz 3:6 is 2 and 10^2÷10^-5 equals 10⁷
Answer:
2×10^7
Step-by-step explanation:
6×10²/3×10^5
6/3×10²-10^-5
2×10²-^(-5)
2×10²+^5
2×10^7
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Does this graph represent a function? Why or why not
One fourth the sum of r and ten is identical to r minus 4.
⇒Mathematically this means
[tex]\frac{1}{4} (r+10)= r-4\\\frac{r}{4} +\frac{10}{4} =r-4\\\frac{r}{4}(4) +\frac{10}{4} (4)=r(4)-4(4)\\r+10=4r-16\\r-4r=-16-10\\-3r=-26\\\frac{-3r}{-3} =\frac{-26}{-3} \\r=\frac{26}{3}[/tex]
Attached is the solution.
2. Mr V bought 2 pajama sets for christmas for $25. He realized that he needed 2 more pajama sets. So now he bought 4 pajama sets for $50. Part A: Is this relationship proportional? Explain. *
We will have that the relationship is proportional because each time he bought more sets they had the same cost, and the total cost added to the sum of the independent cost. And we have the following relationship for the 2 sets and 4 sets:
2 sets:
[tex]\frac{25}{2}=12.5[/tex]So, each individual set is $12.5.
4 sets:
[tex]\frac{50}{4}=12.5[/tex]So, each individual set is $12.5.
So, each individual set for each relationship has the same cost, therefore the relationship is proportional.
a $25$ foot ladder is resting against a wall so that the bottom of the ladder is $7$ feet from the wall. the bottom of the ladder starts slipping away from the wall at a rate of $1$ foot per second. how many feet per second is the top of the ladder sliding down the wall when it is $15$ feet above the ground?
The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. When the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.
Given that,
The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. A feet per second of the ladder's bottom begins to slide away from the wall.
We have to find when the ladder is 15 feet above the ground, how many feet per second is the top of the ladder falling down the wall.
Let us take x = height where the ladder hits the building
7 squared + x squared=25 squared
49+x squared=625
x squared=576
x=24 feet
Now,
If it slips 15 feet that 24-15=9 feet
Let x = distance from wall:
x² + 9² = 25²
x² + 81= 625
x² = 544
x = 23.3 feet
Therefore, when the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.
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Isabella is making bread. She has 7/2 cups of flour. each loaf uses 3/4 cup of flour. How many whole loaves of bread can Isabella make? will she have flour left over?
A. 5 loaves with flour left over.
B. 5 loaves with no flour left over.
C. 4 loaves with flour left over.
D. 4 loaves with no flour left over.
Please help
Answer: C. Four loaves, with flour left over.
Step-by-step explanation:
7/2 simplifies to 3 1/2
Do the math,
3/4 + 3/4 = 1 1/2 2 loaves
1 1/2 + 3/4 = 2 1/4 3 loaves
2 1/4 + 3/4 = 3 4 loaves
Now when we add 3/4 to 3, we get more than 3 1/2. Which means we do not have enough flour for another loaf of bread. So, we can make four loaves and still have some four left over. The answer is C.
of all postsecondary degrees awarded in the united states, including master's and doctorate degrees, 21% are associate's degrees, 58% are earned by people whose race is white, and 12% are associate's degrees earned by whites. what is the conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree? give your answer to three decimal places.
The conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree, is 0.571.
The percentage of associate's degrees is 21%.
The percentage of degrees earned by people whose race is white is 58%.
The percentage of associate's degrees out of all degrees earned by people whose race is white is 12%.
Let the probability of earning an associate's degree be P(A).
P(A) = 0.21
Let the probability of earning a degree by the people whose race is white be P(B).
P(B) = 0.58
Let the probability of earning an associate's degree by the people whose race is white be P(C).
P(C) = 0.12
P(C) = P(A∩B)
We need to find the conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree.
P(B/A) = P(A∩B)/P(A)
P(B/A) = 0.12/0.21
P(B/A) = 0.571
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what is the slope of any line parallel to the line 8x+9x=3 in the standard (x,y) coordinate plane ?
The slope of the line that is parallel to 8x + 9x = 3 is: -8/9.
What is the Slope of Parallel lines?If two lines are parallel to each other, their slope values is equal to each other. This means the value of "m" in their equation expressed in slope-intercept form as y = mx + b, is the same.
Given the equation of a line in standard form as, 8x + 9y = 3, rewrite this in slope-intercept form:
8x + 9y = 3
8x + 9y - 8x = -8x + 3 [subtraction property of equality]
9y = -8x + 3
9y/9 = -8x/9 + 3/9 [division property of equality]
y = -8/9x + 1/3
The slope of the equation is -8/9. Therefore, the slope of the line that is parallel to the equation 8x + 9y = 3 will also be: -8/9.
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write the following number in standard form: nine hundred twenty-eight
In this kind of problem is better to work backwards. We have the number nine hundred twenty-eigh.
This means that the two last digits are a 2 and a 8, becasue we have a "twenty-eight" = 28
And then, we have "nine hundred" = 900
The number whole, then, is:
[tex]928[/tex]The sum of two consecutive integers is 97. What is the smaller integer?
Answer: 48 is the smaller integer
Step-by-step explanation: 48+49=97 48 and 49 are the two integers, 48 is smaller than 49.
which plan will result in the prive of feed reaching 12 faster
In plan B the price rises by 10%.
Thus the price rise is per week is $0.8
In plan A the price rise per week is $0.1
In plan C the price rise per week is
[tex]\frac{12-8}{8}=\frac{4}{8}=0.5[/tex]In plan D the price rise per week is $0.25
Considering all the plan the maximum price rise for each week is 0.8.
So the plan that would lead to $12 fastest is plan B.
The answer is plan B.
Tara makes two batches of purple food coloring. The table show the number of drops of red and blue coloring she uses for each batch. Do the two batches use the same number of drops of red per drop of blue.
Given data:
The number of red drops for first batch are r=100.
The number of blue drops for first batch are b=20.
The number of red drops for second batch are r'=75.
The number of blue drops for second batch are b'=15.
The expression for the red per blue drop for first batch is,
n=r/b
Substitute the given values in the above expression.
n=100/20
=5
The expression for the red drop per blue drop of the second batch is,
n'=r'/b'
Substitute the given values in the above expression.
n'=75/15
=5
Thus, yes the ratio of red to the blue drop is same for both batches.
Find the volume of a cone with radius 8 and height 4.
The volume of the cone is:
[tex]85.33\pi[/tex]Explanation:The volume of a cone is given by the formula:
[tex]V=\frac{1}{3}\pi r^2h[/tex]Given radius, r = 8, and height, h = 4, we have:
[tex]\begin{gathered} V=\frac{1}{3}\pi(8^2)(4) \\ \\ =\frac{256}{3}\pi \\ \\ =85.33\pi \end{gathered}[/tex]Find the value of each variable
Answer:
y=9
Step-by-step explanation:
16y and 18y-18 are vertical angles. The definition of Vertical Angles states that both of the measures of the angles are equal to each other. Therefore,
18y-18=16y
2y-18=0
2y=18
y=9
Any body know the answer to this question?
The curves are intersecting at (1, 1) and (-10, -4)
Nonlinear functions are the functions where the equations are not linear or the highest degree is more than 1. The following are some examples where the functions are not linear or non-linear. Ex. [tex]x^{2}[/tex] + 4x -1
In the above question, a graphical representation of non-linear system of equations is given
We need to find the solution of this non-linear system of equations based on the graphical representation
We can find the solutions from the graph, wherever the curves are intersecting, that intersection point is known as the solution of the non-linear system of equations
We can clearly see that, the curves are intersecting at
(1, 1) and (-10, -4)
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The curves are intersecting at (1, 1) and (-10, -4)
Nonlinear functions are the functions where the equations are not linear or the highest degree is more than 1. The following are some examples where the functions are not linear or non-linear. Ex. [tex]x^{2}[/tex] + 4x -1
In the above question, a graphical representation of non-linear system of equations is given
We need to find the solution of this non-linear system of equations based on the graphical representation
We can find the solutions from the graph, wherever the curves are intersecting, that intersection point is known as the solution of the non-linear system of equations
We can clearly see that, the curves are intersecting at
(1, 1) and (-10, -4)
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How do I get n from 2n C n =70?
After evaluating the expression, the value of n is √(70/2C).
What are expressions?An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) You can think of expressions as being similar to phrases.So, 2nCn = 70:
Now, solve for n as follows:
2nCn =702Cn² = 70n² = 70/2Cn = √(70/2C)Therefore, after evaluating the expression, the value of n is √(70/2C).
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Which logical argument could you use to prove that triangle ABC is congruent to triangle DEF?
A. SSS Postulate
B. HL Theorem
C. SAS Postulate
D. ASA Postulate
tell me if the way I did it includes what's in this equation like if its commutative, associative, distributive or combined like terms
On the first line the distributive property was used. This property says that the product of a constant with a sum of two numbers is equal to the sum of the products.
On the third line the "associative" property was used. This property says that if you have the sum of three numbers the order at which you sum them doesn't affect the results.
A segment is m units long. Find the distance between the midpoints of the first and last parts if the segment is divided into 5 equal parts.
The midpoints of the first and last parts are 4/5m units apart
How to determine the distance between the midpoints?The length of the line segment is given as
Length = m units
From the question, the number of partitions is given as
Partition = 5
So, the length of each partition is
Each partition = Length/Partition
This gives
Each partition = m/5
The midpoint of a partition is
Partition midpoint = m/5 x 1/2
Evaluate
Partition midpoint = m/10
The distance between the midpoints of the first and last segments is then calculated as
Distance = Length - 2 x Partition midpoint
So, we have
Distance = m - 2 x m/10
Evaluate
Distance = m - m/5
This gives
Distance = 4/5m
Hence, the distance is 4/5m units
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Amy has a piece of wood that measures 42 inches. The model shows the length remaining after she cut a piece from the 42-inch piece of wood. About how many inches did Amy cut from the 42-inch piece of wood? 2 3 4 5 6 7 8 10 12 inches
Given data
Ammy has a piece of wood that measures 42 inches
Ammy cut from the 42-inch piece of wood is calculated as
[tex]42-9=33\text{ inches}[/tex]Thus, Amy cut from the 42-inch piece of wood is 33 inches
What is 7h+(-9.1d)-13+6d-3.5h simplified
After simplification, 7h+(-9.1d)-13+6d-3.5h is 3.5h-3.1d-13.
According to the question,
We have the following expression:
7h+(-9.1d)-13+6d-3.5h
Now, we will simplify it by adding or subtracting the numbers or the numbers with the same variable together. For example, 3.5h can only be subtracted from 7h because both of them h as a variable. And 6d can be subtracted from 9.1d.
(More to know: when a positive and a negative number is multiplied then the result is always negative. In this case, we will multiply +1 into -9.1d.)
Now, let's simplify the given expression:
7h-3.5h-9.1d+6d-13
3.5h-3.1d-13
Hence, the expression obtained after solving the given expression is 3.5h-3.1d-13.
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Please help I need answers right now plsssss. The angle of elevation to a nearby tree from a point on the ground is measured to be 54 degrees . How tall is the tree if the point on the ground is 52 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.
Using the angle of elevation, the height of the tree is 71.57 feet.
How to find the height of the tree using angle of elevation?The angles of elevation to a nearby tree from a point on the ground is measured to be 54 degrees.
The distance from the tree to the point on the ground is 52 feet.
The height of the tree can be found as follows:
The situation can be modelled to a right triangle.
Therefore, the height of the tree is the opposite side of the right triangle formed.
Hence,
tan ∅ = opposite / adjacent
where
∅ = angle of elevation
tan 54 = h / 52
cross multiply
h = 52 tan 54
h = 52 × 1.37638192047
h = 71.5718598645
Therefore,
height of the tree = 71.57 feet.
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robert has 30 socks in his sock drawer. 16 of the socks are white, 6 are black, 2 are red, and 6 are yellow.what is the prbability that he randomly pulls out a black sock
The Probability that Robert randomly pulls out a black sock is 1/5 .
In the question ,
it is given that
Total number of socks in sock drawer = 30 socks
number of white socks in the drawer = 16 socks
number of black socks in the drawer = 6 socks
number of red socks in the drawer = 2 socks
number of yellow socks in the drawer = 6 socks
So , the probability that he randomly pulls out a black sock = (number of black socks in the drawer) / ( total number of socks in the drawer )
= 6 / 30
= 1/5
Therefore , The Probability that Robert randomly pulls out a black sock is 1/5 .
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Which equations pass through the points (1, 3) and (7 9)?
Answer:
f(x)=x+2 Passes through
x-y=2 DOES NOT pass through
Step-by-step explanation:
Method- plug in x and see if the y matches the points. (1,3) (7,9)
f(x)=x+2
f(1)=1+2=3
f(7)=7+2=9
Matches!
x-y=2
1-y=2 --> y=-1
Does not match
The net of a rectangular prism is shown below. The surface area of each face is labeled.
We will have the following:
Inferring from the information presented in the diagram we can conclude that the measurements will be:
Base: 3ft * 12ft = 36f t^2
Side1: 3ft * 2ft = 6 ft^2
Side 2: 12ft * 2ft = 24 ft^2
So, the values that would represent the dimension will be:
Length: 12 ft.
Width: 3 ft.
Height: 2 ft.
The formula written in symbols as T =UN. Solve the formula for U.
The formula written in symbols as T =UN. Solve the formula for U.
we have
T=U*N
solve for U
so
isolate the variable U
step 1
divide by N both sides
T/N=U*N/N
T/N=U
therefore
U=T/NWhich answer seems the most reasonable answer to the problem below? *
(-5.6) (3.4) =
-20
18
-15
12
Answer:
-20
Step-by-step explanation:
1- each of the two numbers are inside parenthesis and are beside each other which means they should be multiplied like this: -5.6 * 3.4
2- because 5.6 is negative, the rule in multiplying different signs would result to a negative number
3- and when you accurately multiply them, the answer is 19.04, and the options here are estimated so you should estimate the 19.04 too
4- 1 after it is 9 and nine is a great number, 1 turns to 2 and 9 turns into 0, which equals to 20, and DO NOT forget to add the sign, which is negative as i said previously
29 + 17w = 624
w =
Help
Answer:
w = 35
Step-by-step explanation:
To solve this problem, you will need to undo it in reverse order. The first thing done to w is to multiply it by 17 and then add 29 to it. You need to undo the addition of 29 with subtraction first.
624-28=595
Next, you need to undo the multiplication by 17 with division.
[tex]\frac{595}{17} =35[/tex]
Therefore, your answer is 35
Can someone help me with this
Answer:
1st one- 4
2nd one- 1
3rd one- 5
4th one-6
5th one-3
6th one-2
the difference between the are of arc length and area of a sector please include the formulas for both in your answer
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