Find the average rate of change of f(x) = 3(2)^x between x = 1 and x = 4
Answer:The average rate of change is 14
Solution:The rate of change is given by formula:
[tex]\text { Average Rate }=\frac{f(b)-f(a)}{b-a}[/tex]
Here the given interval is x = 1 and x = 4
Therefore, the formula becomes,
[tex]\text { Average Rate }=\frac{f(4)-f(1)}{4-1}\\\\\text { Average Rate }=\frac{f(4)-f(1)}{3}[/tex]
Let us find f(4) and f(1)
Given function is:
[tex]f(x)=3(2)^x[/tex]
Substitute x = 4 in function
[tex]f(4)=3(2)^4\\\\f(4) = 3 \times 16 = 48[/tex]
Thus f(4) = 48
Substitute x = 1 in function
[tex]f(1) = 3(2)^1\\\\f(1) = 6[/tex]
Now substitute the values back into formula
[tex]\text { Average Rate }=\frac{f(4)-f(1)}{3}\\\\\text { Average Rate }= \frac{48-6}{3}\\\\\text { Average Rate }= 14[/tex]
Thus average rate of change is 14
A square table has an area of "2116" square inches. A tablecloth hang 3 inches over each end of the table, What is the area of the part of the tablecloth that hangs over the table?
The area of the part of the tablecloth that hangs over the table is 285 square inches
Step-by-step explanation:
In order to find the area of table cloth that hangs over the table, we have to find the area of table and the total area of table cloth.
Given
Area of table = [tex]A_t = 2116\ in^2[/tex]
To find the side of the square
[tex]A_t = s^2\\s^2 = 2116[/tex]
Taking Square root on both sides
[tex]\sqrt{s^2} = \sqrt{2116}\\s = 46\ inches[/tex]
When the table cloth is hanged, 3 inches are left to hang over this means that the side will now be: 46+3 = 49 inches
The area of table cloth = [tex]A_c = 49*49 = 2401\ in^2[/tex]
The area of table cloth that will be hung over the table is:
[tex]A_c-A_t\\= 2401-2116\\= 285\ in^2[/tex]
Hence,
The area of the part of the tablecloth that hangs over the table is 285 square inches
Keywords: Square, side
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Graph the equation by plotting three
points. If all three are correct, the line
will appear.
-3y = 2x - 7
Answer:
Step-by-step explanation:
there's your graphed line
credits to desmos graphing calculator
I need help with this question
19. A county government says that a safe level of chlorine in a hot tub is within 1.75 ppm of 3.25 ppm.
a. Write and solve an absolute value inequality to represent this situation
b. A life guard measures the chlorine level in the pool and finds it is 1.0ppm. Should he add more chlorine? Explain.
To ensure safe chlorine levels in the pool, the inequality |Cl - 3.25| ≤ 1.75 must be met, representing levels between 1.50 ppm and 5.00 ppm. The lifeguard found the level at 1.0 ppm, which is below the safe range, so more chlorine needs to be added.
Explanation:Absolute Value Inequality for Chlorine Levels:
The county government specifies that a safe level of chlorine is within 1.75 ppm of 3.25 ppm. We can express this using an absolute value inequality to represent the acceptable range for the chlorine levels: |Cl - 3.25| ≤ 1.75. This represents that the chlorine level (Cl) can be at most 1.75 ppm above or below 3.25 ppm.
To solve this inequality, we consider both the upper and lower bounds:
Therefore, the chlorine level must be between 1.50 ppm and 5.00 ppm.
Analysis of the Chlorine Level Measurement:
As the lifeguard measures the chlorine level in the pool at 1.0 ppm, it falls below the acceptable range established by the inequality. Consequently, the lifeguard should add more chlorine to bring the concentration up to within the safe range, specifically, at least to the minimum safe level of 1.50 ppm.
Help please time limit...Amanda is choosing between two exercise routines.
In Routine #1, she does only running, 15.5 burning calories per minute.
In Routine #2, she burns 22 calories walking. She then runs at a rate that burns 12.75 calories per minute.
For what amounts of time spent running will Routine #1 burn more calories than Routine #2?
Use t for the number of minutes spent running, and solve your inequality for ..
Amanda must spend more than 8 minutes on Routine #1 to burn more calories than Routine #2.
Step-by-step explanation:
Routine # 1;
Calories burned in running = 15.5 per minute
Let,
t be the minutes spent running.
T = total calories burned
T = 15.5t
Routine # 2;
Calories burned while walking = 22 calories
Calories burned while running = 12.75 per minute
T = 12.75t + 22
For burning more calories in Routine 1;
Routine 1 > Routine 2
[tex]15.5t>12.75t+22\\15.5t-12.75t>22\\2.75t>22\\[/tex]
Dividing both sides by 2.75
[tex]\frac{2.75t}{2.75}>\frac{22}{2.75}\\t>8[/tex]
Amanda must spend more than 8 minutes on Routine #1 to burn more calories than Routine #2.
Keywords: linear inequality, division
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Picture attached please help!! I don't understand these questions.
Answer:
a, e
Step-by-step explanation:
a. function A has a slope of -2/3. the negative means it goes down. function B is going down on the graph so both functions have neg. rates of change.
b. function A's slope is -2/3. function b has a slope of -1.
c. since both functions slopes aren't the same they are not parallel.
d. 2/3 is a lesser rate of change than 1.
e. looking at the graph, function b is linear. A is linear since the "x" is not squared, cubed, etc.
If 5x - 3y = 1 and x = 2y - 4, then x • y = ?
I don’t need an explanation of the answer since it’s multiple choice, but feel free to give an explanation if you want :) thank you and please answer quickly this is due tomorrow!!
Answer:
x = 2, y = 3
Step-by-step explanation:
i) It is given that 5x - 3y =1
ii) It is also given that x = 2y - 4
iii) we can substitute the value of x from ii) in the equation in i) and we will get 5(2y - 4) - 3y = 1 ⇒ 10y - 20 -3y = 1 ⇒ 7y = 21 ∴ y = 3
iv) substituting the value of y obtained in ii) we get x = (2 × 3) - 4 = 6 - 4 = 2.
v) Therefore x = 2.
The ratio of the number of flowers in basket A to the number of fliers in basket B is 5:2. If there are 40 flowers in basket B
Answer:
there would be 100 flowers in basket a
Step-by-step explanation:
for the second part of the ratio to be 40 you have to multiply the 2 by 20. to find out how many would be in basket a you do the same thing to the other side of the ratio and multiply 5 by 20 which gives you 100
What is the they answer for
5+4(n+9)=-3
Answer:x=-11
Step-by-step explanation:
The sum of twice a number and half the number is 10.
how would i write the equation?
66pts
Hello there i hope you are having a good day :) Your question : The sum of twice a number and half the number is 10.
Answer would be : 2x + x/2 = 10
Hopefully that helps you ❤
Answer:
2x+x/2 = 10
Step-by-step explanation:
x is the unknown value.
2x would be used to represent the unknown value of twice that number.
/2 would be used to represent half the number.
Hope this helps you!
If 24 people have the flu out of 360 people, how many would have the flu out of
900?
If 24 people have the flue out of 360 people then out of 900, 60 people would have flue if solved through percentage.
What is a percentage?It is a ratio expressed as a fraction of 100. it's expressed using the sign %.
How to calculate percentage?The percentage of individuals gets affected from flue out of 360 is 24*100/360
=2400/360
=6.67%
Then per 6.67% out of 900 approx 60 (900*6.67%) people would be affected from flue.
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If the base angles of an isosceles triangle each measure 37° then the vertex angle measures 106°
Answer:
the given statement is true.
Step-by-step explanation:
i) It is given that the base angles of an isosceles triangle each measure 37°.
ii) Adding the values of the base angles is = 37° + 37° = 74°
iii) from the property of triangles we know that the sum of all the angles in a triangle is equal to 180°
iv) let the vertex angle be = y°
v) Therefore we can say from ii), iii) and iv) above that
74° + y° = 180°
vi) therefore the vertex angle y = 180° - 74° = 106°
Hence the given statement is true.
How do you solve 9+x/9=7/3
Answer:
-60
Step-by-step explanation:
9+x/9=7/3
x/9=7/3-9
x/9=7/3-27/3
x/9=-20/3
x=(-20/3)(9)
x=-180/3
x=-60
1/4 of 1% expressed as a decimal
Answer:
0.0025
Step-by-step explanation:
:)
1/4 of 1%, when expressed as a decimal, is equal to 0.0025
What do we mean by percentage?A percentage is a ratio with the second part always equal to 100. It represents parts per hundred.
How do we solve the given question?We have been given 1%.
We replace percentage in fraction, and then fraction to decimal.
1% = 1/100 = 0.01
Now, we need to calculate 1/4th of this value, that is, 0.25 multiplied by the above value,
= 0.25 * 0.01 = 0.0025
So, our answer is 0.0025.
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what of the following is not a characteristic of all parallelograms diagonals bisect each other be opposite angles are congruent C diagonals are angle bisectors deep is the sides are congruent
The correct option that is not a characteristic of all parallelograms is C, 'diagonals are angle bisectors,' as it does not apply to every parallelogram, unlike the other options listed.
Explanation:The question is related to the properties of parallelograms, and specifically, it asks which option is not a characteristic of all parallelograms. To answer this, we must review the properties of parallelograms:
Diagonals bisect each other.Opposite angles are congruent.The sides are parallel, but not necessarily congruent.Option A (Diagonals bisect each other) and Option B (Opposite angles are congruent) are indeed true characteristics of parallelograms. However, diagonals being angle bisectors is not a general characteristic of all parallelograms, making it incorrect for Option C. Finally, Option D (The sides are congruent) describes a property specific to a rectangle or a rhombus rather than all parallelograms. Thus the correct answer is C, diagonals are angle bisectors, as it is not a defining feature for all parallelograms. Parallelograms have diverse shapes like rectangles, squares, and rhombi, and this property doesn't apply universally.
Select 3 expressions that have a sum or difference of 3 /4 .
A . 1/2 + 2/4
B . 11/12 − 1/6
C. 3/5 + 3/20
D . 7/8 − 1/2
E . 2/3 + 1/12
Answer:
The Three expressions that have a sum or difference of 3 /4 .
B . 11/12 − 1/6
C. 3/5 + 3/20
E . 2/3 + 1/12
Step-by-step explanation:
The Three expressions that have a sum or difference of 3 /4 .
are
B . 11/12 − 1/6
[tex]\dfrac{11}{12}-\dfrac{1}{6}=\dfrac{11}{12}-\dfrac{1\times 2}{6\times 2}\\\\\dfrac{11}{12}-\dfrac{1}{6}=\dfrac{11}{12}-\dfrac{2}{12}=\dfrac{11-2}{12}=\dfrac{9}{12}=\dfrac{3}{4}[/tex]
Therefore,
[tex]\dfrac{11}{12}-\dfrac{1}{6}=\dfrac{3}{4}[/tex]
C. 3/5 + 3/20
[tex]\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{3\times 4}{5\times 4}+\dfrac{3}{20}\\\\\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{12}{20}+\dfrac{3}{20}=\dfrac{15}{20}=\dfrac{3}{4}[/tex]
Therefore,
[tex]\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{3}{4}[/tex]
E . 2/3 + 1/12
[tex]\dfrac{2}{3}+\dfrac{1}{12}=\dfrac{2\times 4}{3\times 4}+\dfrac{1}{12}\\\\\dfrac{3}{5}+\dfrac{3}{20}=\dfrac{8+1}{12}=\dfrac{9}{12}=\dfrac{3}{4}[/tex]
Therefore,
[tex]\dfrac{2}{3}+\dfrac{1}{12}=\dfrac{3}{4}[/tex]
Expressions B (11/12 − 1/6), C (3/5 + 3/20), and E (2/3 + 1/12) each simplify to a sum or difference of 3/4 after finding a common denominator and simplifying the fractions.
Explanation:To find 3 expressions that have a sum or difference of 3/4, let's evaluate each option given:
A. 1/2 + 2/4 simplifies to 1/2 + 1/2, which equals 2/2 or 1. This does not equal 3/4.B. 11/12 − 1/6 can be calculated by finding a common denominator, which would be 12. So, 1/6 is equivalent to 2/12. Thus, 11/12 − 2/12 equals 9/12, which simplifies to 3/4.C. 3/5 + 3/20 requires us to find a common denominator, which would be 20. So, 3/5 is equivalent to 12/20. Thus, 12/20 + 3/20 equals 15/20, which simplifies to 3/4.D. 7/8 − 1/2 requires a common denominator, which would be 8. So, 1/2 is equivalent to 4/8. Thus, 7/8 − 4/8 equals 3/8. This does not equal 3/4.E. 2/3 + 1/12 requires a common denominator, which would be 12. So, 2/3 is equivalent to 8/12. Thus, 8/12 + 1/12 equals 9/12, which simplifies to 3/4.Therefore, the three expressions that have a sum or difference of 3/4 are B, C, and E.
There are 6 students that like milk. There is one student who likes water. How many fewer students like water than milk?
Answer:
5
Step-by-step explanation:
if a=(-2 -4) and b=(-8 4) what is the length of AB
Use the distance formula Sqrt ( (x2-x1)^2 +(y2-y1)^2)
Distance = sqrt ( (-8 - -2)^2 +(4- -4)^2)
Distance = sqrt(-6^2 + 8^2)
Distance = sqrt ( 36 + 64)
Distance = sqrt(100)
Distance = 10
The length is 10
Answer: 10 units
Step-by-step explanation: took test hope this helps
If the arc length shown in blue is 21.3 inches, then 0 to the nearest hundredth of a
radian is
Answer: [tex]\theta\approx1.78\ rad[/tex]
Step-by-step explanation:
By definition, the Arc lenght can be calculated with the following formula:
[tex]s=r\theta[/tex]
Where "s" is the Arc lenght, "r" is the radius and [tex]\theta[/tex] is the central angle measured in radians.
From that equation you can solve for [tex]\theta[/tex] dividing both sides of the equation by the radius "r", then:
[tex]\frac{s}{r}=\frac{r\theta}{r}\\\\\theta=\frac{s}{r}[/tex]
According to the information given in the exercise:
[tex]s=21.3\ in[/tex]
And you can identify in the figure that the radius of the circle is:
[tex]r=12\ in[/tex]
Therefore, you can substitute values into the equation:
[tex]\theta=\frac{21.3\ in}{12\ in}[/tex]
Finally, evaluating, you get the following result:
[tex]\theta=1.775\ rad[/tex]
Rounded to the nearest hundredth of a radian:
[tex]\theta\approx1.78\ rad[/tex]
any help would be great
How do you do inverse operation on a fraction ( y/3 ) = -6
[tex]\frac{-1}{18}[/tex]
Solution:
Given expression is [tex]\frac{y}{3}=-6[/tex]
To find the inverse of y.
⇒ [tex]\frac{y}{3}=-6[/tex]
Do cross multiplication.
⇒ y = –6 × 3
⇒ y = –18
Inverse of y means reverse the function.
We know that inverse of y is [tex]\frac{1}{y}[/tex].
⇒ [tex]\frac{1}{y}= \frac{-1}{18}[/tex]
Hence, inverse of y is [tex]\frac{-1}{18}.[/tex]
which quadratic equation equivalent to (x+2)^2+5(x+2)-6=0
Answer:
[tex]\large\boxed{u^2+5u-6=0,\ where\ u=(x+2)}[/tex]
Step-by-step explanation:
[tex](x+2)^2+5(x+2)-6=0\\\\\text{Substitute}\ (x+2)=u:\\\\\underbrace{(x+2)}_{u}^{}^2+5\underbrace{(x+2)}_{u}-6=0\\\\u^2+5u-6=0[/tex]
Answer:
The answer is C
Step-by-step explanation:
How many edges does this figure have?
Answer:
please show the figure
Step-by-step explanation:
Which figure lol looool
Find y if y = -7x -6 and x=5
Answer: -41
Step-by-step explanation:
-7 × 5 = -35
-35 - 6 = -41
Answer:
-41
Step-by-step explanation:
The bodega offers two deals on chicken nuggets. In deal #1 you can buy 5 chicken nuggets for $7.50. In deal #2 you can buy 8 chicken nuggets for $10.00. In which deal is each chicken nugget cheaper.
Answer:
The 2nd deal is better
Step-by-step explanation:
First you divide the chicken nuggets by the price and then find how much one chicken nugget costs. In this case $10 divided by 8 is $1.25 while $7.50 divided by 5 is $1.50. The first deal costs more for one chicken nugget so deal 2 is better
Answer:
deal 2 is better the chicken nuggets are cheaper and you could have more chicken nuggets even though it cost more then deal 1, 1 chicken nugget is cheaper in deal 2 than it is in deal 1 so I think you should go for deal 2 Hope I Helped :)
Step-by-step explanation:
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y
=
−
2
x
2
+
113
x
−
497
y=−2x
2
+113x−497
The company should sell each widget for $28.25, to the nearest cent.
To maximize profit, we need to find the vertex of the parabola represented by the profit equation y = -2x^2 + 113x - 497. Since the coefficient of x^2 is negative, the parabola opens downwards, and the vertex represents the maximum point. The x-coordinate of the vertex of a parabola in the form of y = ax^2 + bx + c can be found using the formula -b/2a.
For the equation y = -2x^2 + 113x - 497, a = -2 and b = 113. Plugging these values into the formula gives us: x = -113 / (2 × -2) = -113 / -4 = 28.25. Therefore, to maximize profit, the company should sell each widget for $28.25, to the nearest cent.
What is the scale factor?
Answer:
the scale factor is by what multiplier has a shape been increased by in size
The sum of two numbers is 15. The first number is half of the second number. What are the two numbers?
Answer:
10 5
Step-by-step explanation:
10 ÷ 2 = 5 and 5 + 10 = 15
Answer:
5 and 10
Step-by-step explanation:
X×Y=15
X=15-Y
X=Y/2
Y/2=15-Y
Add Y to both sides
3Y/2=15
3Y=30
Y=10
X=5
Compute the perimeter of the figure given below. All angles are right angles.
Answer:
44
Step-by-step explanation:
10 + 12 + 4 + 4 + 6 + 8 = 44
The perimeter of the figure is 26 inches.
The perimeter of the figure is the total length of all the sides. To calculate the perimeter, we simply add up the lengths of all the sides:
Perimeter = 6in + 4in + 4in + 12in
Perimeter = 26in
Therefore, the perimeter of the figure is 26 inches.
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a principal that will amout to 150000 for 8 years at 9/1/2 %
The principal amount is 85227.27 and the interest is 64772.73.
Solution:
Given:
Amount (A)= 150000
Number of years (n)= 8
Rate of interest (r)= [tex]9\frac{1}{2}\%=\frac{19}{2}\%[/tex]
To find: The principal (P)
We know that the principal is the sum of amount and interest. That is, [tex]\bold{P+I=A}[/tex]
This can be written as [tex]\bold{I=A-P \rightarrow(1)}[/tex]
The formula of simple interest is [tex]\bold{I=\frac{Pnr}{100} \rightarrow(2)}[/tex]
On equating (1) and (2) we get,
[tex]\Rightarrow\bold{A-P=\frac{Pnr}{100}}[/tex]
On substituting the values we get,
[tex]\Rightarrow\bold{150000-P=\frac{P\times8\times19}{100\times2}}[/tex]
On solving we get,
[tex]\bold{\Rightarrow 150000-P=0.76P}[/tex]
On grouping the like terms together we get,
[tex]\bold{\Rightarrow 150000=0.76P+P}[/tex]
[tex]\bold{\Rightarrow 150000=1.76P}[/tex]
[tex]\bold{\Rightarrow P=\frac{150000}{1.76}}[/tex]
[tex]\bold{\Rightarrow P=85227.2727\approx85227.27}[/tex]
If principal is 85227.27, then the interest will be [tex]\bold{I=150000-85227.27\rightarrow64772.73}[/tex]