The resulting value of the function [j(x+h)-j(x)/h] is 3⁽ˣ⁻¹⁾ ([tex]3^{h}[/tex]-1)/h
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
Given the function expressed as;
j(x) = 3⁽ˣ⁻¹⁾
Required value of the function [j(x+h)-j(x)]/h
We have to determine the function j(x+h) and j(x)
j(x+h) = [tex]3^{(x+h) -1}[/tex]
Substitute the values,
[j(x+h)-j(x)]/h = [ [tex]3^{(x+h) -1}[/tex] - 3⁽ˣ⁻¹⁾ ]/h
⇒ [ [tex]3^{(x-1) +h}[/tex] - 3⁽ˣ⁻¹⁾ ]/h
⇒ [ [tex]3^{(x-1)} \times3^{h}[/tex] - 3⁽ˣ⁻¹⁾ ]/h
⇒ 3⁽ˣ⁻¹⁾ ([tex]3^{h}[/tex]-1)/h
Hence, the equivalent value of the function is 3⁽ˣ⁻¹⁾ ([tex]3^{h}[/tex]-1)/h
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When you mix two colors of paint in equivalent ratios, the resulting color is 1 po always the same. ***How many cups of yellow paint should you mix with 1 cup of blue paint to make the same shade of green?*** cups of cups of blue paint yellow paint 2 10 1 Your answer
Since question is incomplete, I will try my best to complete it my way:
It is given that 2 cups of blue with 10 cups of yellow make up green.
Question asks how many cups of yellow would i need to mix with 1 cup of blue to make same shade of green.
So,
2 cup with 10 cup
We divide each by 2, to get:
2/2 = 1
10/2 = 5
This means:
1 cup with 5 cup
Or,
1 cup blue with 5 cup yellow.
So, we arrive at our answer:
with 1 cup of blue, we need to fix 5 cups of yellow to get same shade of green.
hat is the expected share return given the following macro-economic probabilities? Probability of recession 20% - Share return 5%; Probability of steady state 60% - Share return 10%; Probability of boom 20% - Share return 15%
Based on the probability of the macro-economic probabilities and the share returns, the expected share return can be found to be 10%.
How to find the expected share return?The expected share return based on the economic probabilities can be found by the formula:
= (Probability of recession x Share return in recessions) + (Probability of steady state x Share return in steady state) + (Probability of boom x Share return in boom)
Solving for the expected share return gives:
= (20% x 5%) + (60% x 10%) + (20% x 15%)
= 1% + 6% + 3%
= 10%
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Can you help me complete the proof and also correct any mistakes in my work.
The given information is:
ABCD is a rhombus.
1 Statement: Rhombus ABCD
Reason: given
2. Statement: AB=AD
Reason: Definition of rhombus (all four sides are congruent)
3. Statement: AE=AE
Reason: Reflexive property
4. Statement: BE=DE
Reason: Diagonals bisect each other
5. Statement: Triangle ABE=Triangle ADE
Reason: SSS congruency (Side-Side-Side).
A couple has two children. Let A be the event that their first child is a boy, and note that P(A) = 51.2%. Let B be theevent that their second child is a girl, with P(B) = 48.8%.A and B are independent events. What is the probability that the couple has a first child that is a boy and a second childthat is a girl?Give your answer as a decimal rounded to two decimal places.
Answer:
P(A and B) = 0.25
Step-by-step explanation:
Since P(A) and P(B) are independents events, The probability P(A) and P(B) occurs consecutively is P(A)*P(B):
P(A and B) = P(A)*P(B)
P(A and B) = 0.512*0.488
P(A and B) = 0.25
The mass of a bull is 325 kg. This is 175 kg more than the mass of a calf. The mass of a calf is 107 kg less than the mass of a cow.
Calculate the mass of a cow
Answer:
257 kg
Step-by-step explanation:
Hello!
Given Info:Bull = 325 kgCalf = 175 kg less than BullCow = 107 kg more than the calfCalf:325 - 175150Cow:150 + 107257The mass of the cow is 257 kg.
Curious about people's recycling behaviors, Franco put on some gloves and sifted through some recycling and trash bins. He kept count of the plastic type of each bottle and which bottles are properly dispensed. Correctly placed Incorrectly placed Plastic #2 3 Plastic #4 3 3 What is the probability that a randomly selected bottle is made of plastic #2 or is correctly placed? Simplify any fractions.
Solution
Note: The event here is Mutually Exclusive,, meaning the 2 events can happen at the same time
Total number = 4 + 3 + 3+3 = 13
[tex]\begin{gathered} P\mleft(A\mright)+P\mleft(B\mright)-P\mleft(AnB\mright) \\ \frac{7}{13}\text{ + }\frac{7}{13}-\frac{4}{13} \\ \frac{7+7-4}{13} \\ \frac{10}{13} \end{gathered}[/tex][tex]F\text{inal Answer = }\frac{10}{13}\text{ }[/tex]The graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the range of the function.
The range of the function is determined as 1 ≤ M ≤ 6.5 kg.
What is range of a function?The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Also we can defined a domain of a function as all the possible values that go into a function.
From the graph the range of the function of the mass of the bucket is calculated as follows;
The minimum value of the mass of the bucket = 1
The maximum value of the mass of the bucket = 6.5 kg
The range of the function (mass, M of the bucket) = {1, 2, 3, 4, 5, 6.5 kg}
1 ≤ M ≤ 6.5 kg
Thus, the range of the function includes numbers ranging from 1 to 6.5 kg. That is {1, 2, 3, 4, 5, 6.5 kg}.
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A number divides equally into another number called ______. A.Remainder
B.divisible
C.Multiplier
D.Divisor
Answer: Divisor
Step-by-step explanation:
The the answer to a division problem is called the quotient. The number that is doing the dividing is called the divisor. The number that gets divided up is called the dividend.
Example: If 3 boys ask to mow your yard for $24, then each boy would get $8.
24 divided by 3 is 8. (24 / 3 = 8 )
24 is the dividend (the number getting divided up)
3 is the divisor (the number that is doing the dividing)
8 is the quotient.
Multiple choice triangle. im pretty sure its pythagorean theorem but please let me know
To solve this triangle, we cannot use either the Pythagorean Theorem or the Law of Cosines. We need more information.
Conversely, we can use SOHCAHTOA, in the sense that we can use the SOH part of this (Sine = opposite side over hypotenuse), that is, we can use angle 33 as the reference angle, and we have a right triangle here. Then, using trigonometric ratios, we can use:
[tex]\sin (\theta)=\frac{opp}{hyp}\Rightarrow\sin (33)=\frac{x}{29}\Rightarrow x=29\cdot\sin (33)\Rightarrow x=15.7945[/tex]We also can use the Law of Sines to solve it:
[tex]\frac{x}{\sin(33)}=\frac{29}{\sin(90)}\Rightarrow\frac{x}{\sin(33)}=\frac{29}{1}\Rightarrow x=29\cdot\sin (33)\Rightarrow x=15.7945[/tex]Therefore, we can solve this triangle using both Law of Sines and SOHCAHTOA. (We can select two options: c and d.)
Refer to the number line. Find the coordinate of point X such that the ratio of BX to XF is 3:2
Coordinate of point X such that the ratio of BX to XF is 3:2 is 1 i.e. point D.
What is Coordinate?
A combination of numbers that use the vertical and horizontal separations out from two reference axes to define a point's location on a coordinate plane. Typically expressed by the x-value & y-value pair (x,y).A group of variables that accurately depict a stance.The first number on a graph represents the distance along, while the second number represents the distance upward or downward.Total coordinates son number line from -7 to +7 =15
Number line ratio that has to be provided = 3:2
Let the coordinate be provided is x.
Therefore, 3x+2x=15
⇒5x=15
⇒x=3
Coordinate X
3x=3(3)=9
9th coordinate from -7 = 1 i.e. D
Coordinate of point X such that the ratio of BX to XF is 3:2 is 1 i.e. point D.
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3 c) and 10 d) - and 12 9draw a diagram for each pair of fractions. Which pairs are equivalent? Circle them
Drawing the diagram of option D we have
Which means that 5/6 and 10/12 are equivalent fractions.
m multipled by the square of n
Answer:
mn²
Step-by-step explanation:
the square of n is n² and m multiplied by this is
mn²
You are designing a rectangular poster to contain 70 cm2 of printing with a 2 cm margin at the top and bottom and a 4 cm margin on the left and right. Determine, to two decimal places, the length of the poster required so as to minimize the amount of paper used.
The dimension of minimum paper size would be 18 inches by 9 inches.
What dimensions will minimize the amount of paper used?Let the paper size be x inches in length and y inches in width.
The length of the printed space would be x-8 inches and width would be y-4 inches.
Print area would thus be (x-8)(y-4)=50.
From this [tex]$y=4+\frac{50}{x-8}=\frac{4 x+18}{x-8}$[/tex]
Also from the same equation on simplifying, it is x y-8 y-4 x+32=50.
Since the area of the paper of size x inches by y inches is xy, let it be denoted as A.
Thus
[tex]$A-8 y-4 x=18$[/tex] Or [tex]$A=8 y+4 x+18$[/tex]
[tex]$A=\frac{32 x+144}{x-8}+4 x+18$[/tex].
For minimum paper size [tex]$\frac{d A}{d x}$[/tex] must be =0, hence,
[tex]$\frac{d A}{d x}=\frac{32(x-8)-(32 x+144)}{(x-8)^2}+4=0$[/tex]
[tex]$\frac{-400}{(x-8)^2}+4=0$[/tex]
(x-8)² = 100
x-8 = 10
[tex]$\mathrm{x}=18$[/tex], hence [tex]$\mathrm{y}=4+\frac{50}{x-8}=9$[/tex]
Dimension of minimum paper size would be 18 inches by 9 inches.
The complete question is:
You are designing a rectangular poster to contain 50 in^2 of printing with a 4-in. margin at the top and bottom and a 2-in margin at each side. What overall dimensions will minimize the amount of paper used?
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the store purchased a produce for 1 dollar and sells it for 6 what is the mark up as a precent?
Pls help asap
Answer:
[tex]1 \div 6 = 0.16 \times 100 = 16.6 percent[/tex]
that's all I know
Find the Slope of the line through the points (4, -5) and (2, 2) then graph it.Slope =
The Slope of the line through the points (4, -5) and (2, 2) then graph it. Slope [tex]m=-\frac{7}{2}$$[/tex]
Slope between two points: [tex]$\quad$[/tex]Slope [tex]$=\frac{y_2-y_1}{x_2-x_1}$[/tex]
[tex]$$\begin{aligned}&\left(x_1, y_1\right)=(4,-5),\left(x_2, y_2\right)=(2,2) \\&m=\frac{2-(-5)}{2-4}\end{aligned}$$[/tex]
Refine
[tex]m=-\frac{7}{2}$$[/tex]
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
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-3(x+3)+11=14
(steps included)
Answer:
-4
Step-by-step explanation:
-3(x+3)+11=14
-3·x-3·3+11=14
-3x-9+11=14
-3x+2=14
-3x=14-2
-3x=12
x=12÷(-3)
x=-4
John is a software salesperson. His base salary is $2300 and he makes $70 more for every copy of English is Fun he sells. His total pay, P (in dollars), after selling c copies is given by the following.
P=70c+2300
(a) If john’s total pay is $4750, how many copies did he sell?
(b) What is john’s total pay if he sells 25 copies?
Answer:
A - 35 copies
B - $4050
Step-by-step explanation:
A-
2300 + 70c = 4750
70c = 4750 - 2300
70c = 2450
c = 35
He sold 35 copies
B-
P = 2300 + 70(25)
P = 2300 + 1750
P = $4050
Total if he sold 25 copies: $4050
Find the expected value E(X) of the following data. Round your answer to one decimal place.AnswerHow to enter your answer (opens in new window)6P(X = x) 0.1x789100.2 0.2 0.2 0.3
[tex]E(X)=\Sigma xP(x)[/tex][tex]\begin{gathered} (6\times0.1)+(7\times0.2)+(8\times0.2)+(9\times0.2)+(10\times0.3) \\ \\ =8.4 \end{gathered}[/tex]
Note ; We multiplied each of the x-values with their probabilities and obtain the sum of all. This gives the expected value.
ill give brainliest if i can have help, i am having trouble turning on axis, can someone explain? (refer to image somewhere lol)
Answer:
a=2,-2 b=-5,-1 c=-1,-2
Step-by-step explanation:
you just put the shape the opisite way
Given: GC bisects FGH. Determine the missing measure.a. m
Given that line segment, GC bisects ∠FGH
I made a sketch of the angles, they are not at scale.
That segment GC is an angle bisector indicates that it divides ∠FGH into halves. To determine the measure of the ∠FGC and ∠CGH you have to divide the measure of FGH by 2.
[tex]\angle\text{FGC}=\angle\text{CGH}=\frac{\angle\text{FGH}}{2}[/tex]a) ∠FGH=86º
[tex]\begin{gathered} \angle\text{FGC}=\frac{\angle FGH}{2} \\ \angle\text{FGC}=\frac{86º}{2} \\ \angle\text{FGC}=43º \end{gathered}[/tex]So, in this case, the measure of ∠FGC is 43º.
b) For this item you have to determine the measure of ∠FGH given that the measure of one of the angles determined by the bisector is ∠CGH. To determine the measure of ∠FGH you have to multiply ∠CGH by 2
[tex]\begin{gathered} \angle\text{FGH}=2\cdot\angle\text{CGH} \\ \angle\text{FGH}=2\cdot28º \\ \angle\text{FGH}=56º \end{gathered}[/tex]Sketch the graph of the equation. Label the vertex and the intercepts.
Given,
The expression of the function is,
[tex]y=x^2+4x+3[/tex]Required
The graph of the function.
Take x = 1 then the value of y is,
[tex]y=1^2+4(1)+3=8[/tex]Take x = 2 then the value of y is,
[tex]y=2^2+4(2)+3=15[/tex]Take x = 0 then the value of y is,
[tex]y=(-1)^2+4(-1)+3=0[/tex]Take x = -1 then the value of y is,
[tex]y=1^2+4(1)+3=8[/tex]Take x = -2 then the value of y is,
[tex]y=(-2)^2+4(-2)+3=-1[/tex]The graph of the function is,
The vertex of the graph is (-2, -1).
The x - intercept of the graph is -1 and -3.
The y - intercept of the graph is at 3.
Hence, the graph of the function is obtained.
A fisher finder shows a large fish at 13 ft below the surface and a smaller fish 4 ft below surface. what is the expressions that are equivalent to the distance between the fish
Answer:
Distance = 9 ft
Explanation:
We can represent the position of the large fish with the number -13 because it is 13ft below the surface. In the same way, we can represent the position of the smaller fish with the number -4.
Then, the distance between the fish will be the absolute value of the difference between their positions. So, the expressions that are equivalent to the distance between the fish are:
| - 13 - ( - 4) | = | - 13 + 4| = 9
or
| -4 - (- 13) | = | - 4 + 13 | = 9
Therefore the distance between the fish is 9 ft
Give a formular on how to calculate growth rate
Answer:
Straight-line percent change method example
Growth rate = (489 - 402) / 402. Absolute change = 87 (489 - 402) Growth rate = 0.2164 (87 / 402) Percent change = 21.64% (0.2164 x 100)
Given the graph of a function f. Identify function by name. Then graph the indicated functions. State the domain and the range in set notation.A) f(x-1) -3B) -f(x)
Answer:
For f(x);
The domain is;
[tex]D\colon x=(-\infty,\infty)[/tex]The range is;
[tex]R\colon y=\lbrack0,\infty)[/tex]Graphing those points for function A, we have;
The domain and range of the given function A is;
[tex]\begin{gathered} \text{Domain}\colon x=(-\infty,\infty) \\ \text{Range}\colon y=\lbrack-3,\infty) \end{gathered}[/tex]Graphing those points for function B, we have;
The domain and range of the given function B is;
[tex]\begin{gathered} \text{Domain}\colon x=(-\infty,\infty) \\ \text{Range}\colon y=(-\infty,0\rbrack \end{gathered}[/tex]Explanation:
Given the function in the attached image;
The function is a square function and can be written as;
[tex]f(x)=x^2[/tex]The domain is;
[tex]D\colon x=(-\infty,\infty)[/tex]The range is;
[tex]R\colon y=\lbrack0,\infty)[/tex]A.
[tex]f(x-1)-3=(x-1)^2-3[/tex]B.
[tex]-f(x)=-x^2[/tex]Graphing the functions;
For A;
[tex]\begin{gathered} f(1-1)=(1-1)^2-3=-3 \\ (1,-3) \\ f(3-1)=(3-1)^2-3=1 \\ (3,1) \\ f(-1-1)=(-1-1)^2-3=1 \\ (-1,1) \end{gathered}[/tex]Graphing those points for function A, we have;
The domain and range of the given function A is;
[tex]\begin{gathered} \text{Domain}\colon x=(-\infty,\infty) \\ \text{Range}\colon y=\lbrack-3,\infty) \end{gathered}[/tex]For B;
[tex]\begin{gathered} -f(x)=-x^2 \\ -f(0)=-0^2 \\ (0,0) \\ -f(2)=-2^2=-4 \\ (2,-4) \\ -f(-2)=-(-2)^2=-4 \\ (-2,-4) \end{gathered}[/tex]Graphing those points for function B, we have;
The domain and range of the given function B is;
[tex]\begin{gathered} \text{Domain}\colon x=(-\infty,\infty) \\ \text{Range}\colon y=(-\infty,0\rbrack \end{gathered}[/tex]i need help plsssssssssss ill put 20 points
The common differences of arithmetic sequence are;
For a) -3
For b) - 20
For c) - 30
For d) - 10
What is Arithmetic sequence?
An arithmetic sequence is ordered set of numbers that have common difference between each consecutive term.
Given that;
The Arithmetic sequence are;
a) 35, 32, 29, 26 ...
b) - 3, -23, - 43, -63
c) -34, -64, -94, - 124
d) - 30, - 40, - 50, -60
Now, The common difference of an arithmetic sequence is calculated by the difference between each consecutive term.
For Arithmetic sequence a;
Common difference = 32 - 35 = -3
And, For Arithmetic sequence b;
Common difference = - 23 - (-3)
= - 23 + 3
= - 20
For Arithmetic sequence c;
Common difference = - 64 - (-34)
= - 64 + 34
= - 30
For Arithmetic sequence d;
Common difference = - 40 - (-30)
= - 40 + 30
= - 10
Thus, The common differences of arithmetic sequence are;
For a) -3
For b) - 20
For c) - 30
For d) - 10
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I need to Know how to find the maximum and the minimum values of a function?
Answer:
Step-by-step explanation:
first you need to figure out what your solving for We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.
i dont really get what it means by pattern can u help me understand
Well the principals patterns are that the equations are quadratic equations, and the graphs are parables and that the equations and the graphs are related.
how much of a 2 gram sample of silver-105 would remain after 86 days? round to three decimal places
We know that the half life of this element is 41.3 days.
We have to find how much will remain of a sample of 2 grams after 86 days.
The half life of 41.3 days means that the mass after 41.3 days will become half of what it was.
We can express this as:
[tex]\frac{M(t+41.3)}{M(t)}=\frac{1}{2}[/tex]As this is represented with an exponential model like this:
[tex]M(t)=M(0)\cdot b^t[/tex]we can use the half-life to find the parameter b:
[tex]\begin{gathered} \frac{M(t+41.3)}{M(t)}=\frac{1}{2} \\ \frac{M(0)\cdot b^{t+41.3}}{M(0)\cdot b^t}=\frac{1}{2} \\ b^{t+41.3-t}=\frac{1}{2} \\ b^{41.3}=\frac{1}{2} \\ b=(\frac{1}{2})^{\frac{1}{41.3}} \end{gathered}[/tex]Then, knowing that the initial mass M(0) is 2 grams, we can express the final model as:
[tex]M(t)=2\cdot(\frac{1}{2})^{\frac{t}{41.3}}[/tex]We then can calculate the mass after t = 86 days as:
[tex]\begin{gathered} M(86)=2\cdot(\frac{1}{2})^{\frac{86}{41.3}} \\ M(86)\approx2\cdot0.236 \\ M(86)\approx0.472 \end{gathered}[/tex]Answer: the mass after 86 days will be 0.472 grams.
You have a solution that is 18.5% methyl alcohol. If the bottle contains 1.43 L of solution, what is the volume in milliliters of methyl alcohol?
We have the next given information:
-18.5% is the percentage of methyl alcohol
- The bottle contains 1.43 L
Now, we need to convert the percentage into a decimal.
Then 18.5% = 0.185
We need to determinate the volume in millimeters for methyl alcohol:
If 143L of solution contains 18.5% of methyl alcohol. Therefore:
The volume of methyl alcohol = 1.43 * 0.185
= 0.26455 L
Then, we need to convert Liters to milliliters:
1L ---------------------------- 1000ml
0.26455 L ------------------ x
Where x = (0.26455 L*1000ml)/1L
x =264.55ml
Looking back on your History class, you discovered something interesting. On your first test, you received a score of 65 points with no additional study time, other than doing your homework and attend lectures. On the second test, you decided to put in two additional hours of study time and receive a score of 85. After you have studied some mathematical modeling in math 49, you suspect that there is a relationship between your test score and the number of additional study time. Let S be your test score and T is your additional study time.
A. Assuming S and T have a linear relationship, find a formula for the linear function S=f(T).(12pts)
B. If you want a score of 98. How many hours of additional time of study would you have to put in? (3pts)
Answer:
A. S = 65 + 10x
B. 3.3 hours
Step-by-step explanation:
A. S=f(T)
65 = f(0)
85 = f(2)
S₂ - S₁
85 - 65 = 20
T₂ - T₁
2 - 0 = 2
20 / 2 = 10
For every hour you study, you will score an additional 10 points with a baseline of 65 points.
S = 65 + 10x where x is the amount of time (in hours) that you studied for.
B. S = 65 + 10x
Since we want a specific score of 98, we plug it in for S and solve for x.
98 = 65 + 10x
33 = 10x
3.3 = x
If we wanted a score of 98, we would need to study for 3.3 hours.