You are looking for summer work to help pay for college expenses. Your neighbor is interested in hiring you to do yard work and other odd jobs. You tell them that you can start right away and will work all day July 1 for 3 cents. This gets your neighbor's attention, but they is wondering if there is a catch. You tell them that you will work July 2 for 9 cents, July 3 for 27 cents, July 4 for 81 cents, and so on for every day in the month of July. Which equation will help you determine how much money you will make in July?
Answers
Answer:
y=3^x
Explanation:
The expected payments (in cents) beginning from July 1 are given below:
[tex]3,9,27,81,\cdots[/tex]Observing the payments for each subsequent day, we see that the payment for the previous day was multiplied by 3.
We can rewrite the payment as a power of 3 as follows:
[tex]3^1,3^2,3^3,3^4,\cdots[/tex]Therefore, the equation will help you determine how much money you will make in July will be:
[tex]y=3^x[/tex]The first option is correct.
Related Questions
(statistics) solve part A, B, and C in the question on the picture provide, in 1-3 complete sentences each.
Answers
(a.) First let's define the terms;
Population - it is the pool of individual in which a statistical sample is drawn.
Parameter - it is a measure of quantity that summarizes or describes a Population.
Sample - is a smaller and more managable version of a group or population.
Statistics - same with parameter but rather than the population, it summarizes or describes
the sample.
Now that we know the definitions we can now answe the letter a;
Population: Students
Parameter: the population portion of the new students that like the new healthy choices (p)
Sample: 150 students
Statistics: estimated propotion of the students that like the new healthy choices (p-hat)
(b) P-hat = 0.6267 simply means that 62.67% of the 150 sample students like the new healthy choices.
(c) The answer for that is NO, because the simulated propotion which is shown by the graph seems to be equally distributed below and above 0.7. To support the claim of the manager most of the dots should be below 0.7 to show support to his claim that 70% of the new students like the new healthy choices.
For the compound inequalities below (5-7), determine whether the inequality results in an overlapping region or a combined region. Then determine whether the circles are open are closed. Finally, graph the compound inequality. Simplify if needed. x-1>_5 and 2x<14
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The inequalities are:
[tex]x-1\ge5\text{ and }2x<14[/tex]So, we need to solve for x on both inequalities as:
[tex]\begin{gathered} x-1\ge5 \\ x-1+1\ge5+1 \\ x\ge6 \end{gathered}[/tex][tex]\begin{gathered} 2x<14 \\ \frac{2x}{2}<\frac{14}{2} \\ x<7 \end{gathered}[/tex]Now, we can model the inequalities as:
So, the region that results is an overlapping region and it is written as:
6 ≤ x < 7
So, the lower limit 6 is closed and the upper limit 7 is open.
Answer: The region is overlaping and it is 6 ≤ x < 7
(4 to the 3rd power * 4 to the 6 power)to the 5th power
Answers
hello
if i'm right, what you're trying to ask is
given the parent function f (x) identify whether g (x) is a reflection about a horizontal line of reflection or vertical line of reflectionf (x) = 6^x and g (x) = - (6^x)
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The relation between this two functions is g(x) = -f(x)
This means that g(x) is a reflection of f(x) about the x-axis, that is, a reflection about a horizontal line
8in 8in 8in area of irregular figures
Answers
Given data:
The given figure.
The expression for the area is,
[tex]\begin{gathered} A=(8\text{ in)(8 in)+}\frac{1}{2}(8\text{ in)( 8 in)} \\ =96in^2 \end{gathered}[/tex]Thus, the area of the given ffigure is 96 square-inches.
give the quadratic function a graph for the function f (x)= -(x-3)^2-2
Answers
Answer
The graph of the function f(x) = -(x - 3)² - 2, is presented below
Explanation
We are told to graph a given function
f(x) = -(x - 3)² - 2
The first step into making this easy is to open the bracket.
f(x) = - (x² - 6x + 9) - 2
f(x) = -x² + 6x - 9 - 2
f(x) = -x² + 6x - 11
The next step is then to insert different values of x into the function and obtain the corresponding value of the function. This set of ordered pairs arethen plotted to form the graph.
The graph is then plotted and presented under 'Answers' above.
Hope this Helps!!!
Solve for the Limit of Function by applying appropriate Limit Theorems
Answers
Answer:
Given to solve,
[tex]\lim _{x\to-1}(2x+2)(x+2)[/tex]From the rules for limits, we can see that for any polynomial, the limit of the polynomial when x approaches a point k is equal to the value of the polynomial at k.
The given function of the limit is a quadratic function, the limit of the quadratic equation when x approaches a point -1 is equal to the value of the quadratic equation at -1.
we get,
[tex]\lim _{x\to-1}(2x+2)(x+2)=(2(-1)+2)((-1)+2)[/tex][tex]=(-2+2)(1)=0[/tex][tex]\lim _{x\to-1}(2x+2)(x+2)=0[/tex]
Answer is : 0
the perimeter of the rectangle belowis 112 units. Find the value of y
Answers
Question:
Solution:
The perimeter of a rectangle is the sum of the lengths of its sides. According to this, we get the following equation:
[tex]P\text{ = 2(4y+2)+2(5y)}[/tex]since P = 112, we obtain:
[tex]112\text{ = 2(4y+2)+2(5y)}[/tex]Applying the distributive property, we obtain:
[tex]112\text{ = 8y+4+10y}[/tex]this is equivalent to:
[tex]18y\text{ = 112-4}[/tex]that is:
[tex]18\text{ y = 108}[/tex]solving for y, we get:
[tex]y\text{ = }\frac{108}{18}=6[/tex]that is:
[tex]y\text{ = 6}[/tex]so that, we can conclude that the correct answer is:
[tex]6[/tex]Omaha Beef Company purchased a delivery truck for $66,000. The residual value at the end of an estimated eight-year service life is expected to be $12,000. The company uses straight-line depreciation for the first six years. In the seventh year, the company now believes the truck will be useful for a total of 10 years (four more years), and the residual value will remain at $12,000. Calculate depreciation expense for the seventh year.
Answers
Given:
Company purchased = $66000
Find-:
Depreciation expense for the seventh year
Sol:
First, depreciate for 6 years using the regular method:
[tex]\begin{gathered} =\frac{\text{ Cost - salvage value}}{\text{ initial useful life}} \\ \\ =\frac{66000-12000}{8} \\ \\ =6750 \end{gathered}[/tex]The annual depreciation is 6750.
For 6 years
[tex]\begin{gathered} =6750\times6 \\ \\ =40500 \end{gathered}[/tex]So
[tex]\begin{gathered} \text{ Remaining useful life = 10-6} \\ =4 \\ \\ =\frac{66000-40500-12000}{4} \\ \\ =\frac{13500}{4} \\ \\ =3375 \end{gathered}[/tex]For seventh-year depreciation expense is $3375
The measure of the smallest angle in a right triangle is 45° 45 ° less than the measure of the next larger angle. Find the measures of all three angles.
Answers
Angle A or B must be 90 degrees since it is a right triangle. Given that C is more than 60 and that there are 180 degrees in a triangle, the other angle must be less than 30 degrees.
How to measure the three angles?The smallest angle in a right triangle has a measure that is 45° smaller than the next largest angle.As a result, the other two angles' measurements must sum up to 90. The only solution to this would be for both of the remaining angles to be 45 degrees if the lowest angle is 45 degrees less than the next largest angle. The correct angle would be the next biggest angle.Angle A or B must be 90 degrees since it is a right triangle. Given that C is more than 60 and that there are 180 degrees in a triangle, the other angle must be less than 30 degrees.To learn more about Right triangle refer to:
https://brainly.com/question/2217700
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mark has a bag containing a mixture of 30 green and white marbles.
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SOLUTION:
From the experiment performed;
Mark got 10 green marbles and 5 white marbles after 15 trials. Since the number of green marbles gotten in the experiment is more than the white, the conclusion best supported by the experiment is ;
The bag contains more green than white marbles.
The width of a rectangle is 6 less than twice its length. If the area of the rectangle is 170 cm2 , what is the length of the diagonal?The length of the diagonal is cm.Give your answer to 2 decimal places.Submit QuestionQuestion 25
Answers
The formula to find the area of a rectangle is:
[tex]\begin{gathered} A=l\cdot w \\ \text{ Where} \\ \text{ A is the area} \\ l\text{ is the length} \\ w\text{ is the width} \end{gathered}[/tex]Since the rectangle area is 170cm², we can write the following equation.
[tex]170=l\cdot w\Rightarrow\text{ Equation 1}[/tex]On the other hand, we know that the width of the rectangle is 6 less than twice its length. Then, we can write another equation.
[tex]\begin{gathered} w=2l-6\Rightarrow\text{ Equation 2} \\ \text{ Because} \\ 2l\Rightarrow\text{ Twice length} \\ 2l-6\Rightarrow\text{ 6 less than twice length} \end{gathered}[/tex]Now, we solve the found system of equations.
[tex]\begin{cases}170=l\cdot w\Rightarrow\text{ Equation 1} \\ w=2l-6\Rightarrow\text{ Equation 2}\end{cases}[/tex]For this, we can use the substitution method.
Step 1: we replace the value of w from Equation 2 into Equation 1. Then, we solve for l.
[tex]\begin{gathered} 170=l(2l-6) \\ \text{Apply the distributive property} \\ 170=l\cdot2l-l\cdot6 \\ 170=2l^2-6l \\ \text{ Subtract 170 from both sides} \\ 0=2l^2-6l-170 \end{gathered}[/tex]We can use the quadratic formula to solve the above equation.
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\Rightarrow\text{ Quadratic formula} \\ \text{ For }ax^2+bx+c=0 \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} a=2 \\ b=-6 \\ c=-170 \\ l=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ l=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(2)(-170)}}{2(2)} \\ l=\frac{6\pm\sqrt[]{1396}}{4} \\ \end{gathered}[/tex]There are two solutions for l.
[tex]\begin{gathered} l_1=\frac{6+\sqrt[]{1396}}{4}\approx10.84 \\ l_2=\frac{6-\sqrt[]{1396}}{4}\approx-7.84 \\ \text{ The symbol }\approx\text{ is read 'approximately'.} \end{gathered}[/tex]Since the value of l can not be negative, the value of l is 10.84.
Step 2: We replace the value of l into any of the equations of the system to find the value of w. For example, in Equation 1.
[tex]\begin{gathered} 170=l\cdot w\Rightarrow\text{ Equation 1} \\ 170=10.84\cdot w \\ \text{ Divide by 10.84 from both sides} \\ \frac{170}{10.84}=\frac{10.84\cdot w}{10.84} \\ 15.68\approx w \end{gathered}[/tex]Now, the long side, the wide side and the diagonal of the rectangle form a right triangle.
Then, we can use the Pythagorean theorem formula to find the length of the diagonal.
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where} \\ a\text{ and }b\text{ are the legs} \\ c\text{ is the hypotenuse} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} a=10.84 \\ b=15.68 \\ a^2+b^2=c^2 \\ (10.84)^2+(15.68)^2=c^2 \\ 117.51+245.86=c^2 \\ 363.37=c^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{363.37}=\sqrt[]{c^2} \\ 19.06=c \end{gathered}[/tex]Therefore, the length of the diagonal of the given rectangle is 19.06 cm rounded to 2 decimal places.
Find the perimeter of with vertices A(1, –3), B(7, –3), and C(1, 5).
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This is a triangle with 3 vertices given.
I need help with this problem.
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Using tangent function:
[tex]\begin{gathered} \tan (\theta)=\frac{opposite}{adjacent} \\ \tan (T)=\frac{16}{32}=\frac{1}{2}=0.5 \end{gathered}[/tex]How many rays are in the next two terms in the sequence?
Answers
The sequnce is
2, 3, 5, 9, ....
this sequence follows the next formula:
[tex]a_n=2^{n-1}+1[/tex]where an is the nth term.
[tex]\begin{gathered} a_1=2^{1-1}+1=1 \\ a_2=2^{2-1}+1=3 \\ a_3=2^{3-1}+1=5 \\ a_4=2^{4-1}+1=9 \\ a_5=2^{5-1}+1=17 \\ a_6=2^{6-1}+1=33 \end{gathered}[/tex]The next two terms are 17 and 33
Translate this phrase into an algebraic expression.72 decreased by twice a numberUse the variable n to represent the unknown number.
Answers
When the questions uses the word "decreased" this means that a value was subtracted by another value. The word "twice" symbolizes that a number was doubled or multiplied by 2. With this understanding, we can create the expression:
[tex]72-2n[/tex]Let MF = 3x - 4 and BM = 5x - 5
Answers
Answer:
Explanation:
a)Here, we want to get the value of x
Mathematically, we know that for a triangle with median M, the length of one of the sides is two times the length of the other side of the median
We have this as:
[tex]BM\text{ }=\text{ 2MF}[/tex]Using the side lengths given, we have it that:
[tex]\begin{gathered} 5x-5\text{ = 2(3x-4)} \\ 5x-5\text{ = 6x-8} \\ 6x-5x=8-5 \\ x\text{ = 3} \end{gathered}[/tex]b) We want to find the length of MF. We just have to substitute the value of x in the expression for MP
Mathematically, we have this as:
[tex]MF\text{ = 3(3)-4 = 9-4 = 5}[/tex]c) We want to find the length of BM
[tex]5x-5\text{ = 5(3)-5 = 15-}5\text{ = 10}[/tex]d) Here, we want to find the length of BF
[tex]\begin{gathered} BF\text{ = BM + MF} \\ BF\text{ = 10 + 5 = 15} \end{gathered}[/tex]in the diagram triangle JKL and is inscribed in the circle and Arc JL = 62 degrees what is angle L
Answers
SOLUTION
m < L = ?
m < J = 62 degrees
m < L + 62 + 90 = 180 ( Sum of angles in a triangle )
m < L + 152 = 180
m < L = 180 - 152
[tex]4(2 \times - 1) \ \textless \ (4 \times - 3)[/tex]That is the Math problem
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Hello I I am confused because their are two different letters.
Answers
Let's begin by listing out the information given to us:
Line AB is parallel to Line CD; this implies that the angle formed by the two lines are right angles (90 degrees)
E is the intersecting point of both lines AB & CD (figure attached)
Let us put this into its mathematical form:
[tex]\begin{gathered} m\angle AED=(6x-24)=90^{\circ} \\ 6x-24=90\Rightarrow6x=90+24 \\ 6x=114\Rightarrow x=19 \\ x=19 \\ m\angle CEB=(4y+32)=90^{\circ} \\ 4y+32=90\Rightarrow4y=90-32 \\ 4y=58\Rightarrow y=17 \\ y=17 \end{gathered}[/tex]I survey found that 43 people like chocolate 39 people like peanut butter and 29 people like both draw an empty van diagram with intersections find how many people like only chocolate only peanut butter and both show your work fill in the V diagram according your numbers Calculate how many people are in the survey
Answers
Given:
There are 43 people who like chocolate 39 people like peanut butter and 29 people like both.
To draw: The ven diagram
Explanation:
Since 29 people like both chocolate and peanut butter.
Therefore,
The number of people who like chocolate only is,
[tex]43-29=14[/tex]The number of people who like peanut butter only is,
[tex]39-29=10[/tex]So, the total number of persons is,
[tex]14+29+10=53[/tex]The ven diagram is,
Where C represents the chocolate likers, B represents the peanut butter likers and U represents the total number of persons.
Final answer:
• The number of people who like chocolate only is 14.
,• The number of people who like peanut butter only is 10.
,• The total number of people is 53.
At Bright Futures Middle School, 576 students ride their bike to school . If this number is 75% of the school enrollment, then how many students are enrolled
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
students on bike = 576
% students on bike = 75%
total students = ?
Step 02:
total students
[tex]\text{ \% students on bike = }\frac{students\text{ on bike }}{\text{total students }}\cdot100[/tex][tex]\begin{gathered} 75\text{ = }\frac{576}{\text{total students }}\cdot100 \\ \text{total students = }\frac{576}{75}\cdot100 \end{gathered}[/tex]total students = 768
The answer is:
The number of total students is 768.
Hello! I need some help with this homework question, please? The question is posted in the image below. Q6
Answers
Step 1
Given;
[tex]g(x)=3x^2-5x-2[/tex]Required; To find the zeroes by factoring
Step 2
Find two factors that when added gives -5x and when multiplied give -6x
[tex]\begin{gathered} \text{These factors are;} \\ -6x\text{ and x} \end{gathered}[/tex][tex]\begin{gathered} -6x\times x=-6x^2 \\ -6x+x=-5x \end{gathered}[/tex]Factoring we have and replacing -5x with -6x and x we have
[tex]\begin{gathered} 3x^2-6x+x-2=0 \\ (3x^2-6x)+(x-2)_{}=0 \\ 3x(x-2)+1(x-2)=0 \\ (3x+1)(x-2)=0 \\ 3x+1=0\text{ or x-2=0} \\ x=-\frac{1}{3},2 \\ \text{The z}eroes\text{ are, x=-}\frac{1}{3},2 \end{gathered}[/tex]Graphically the x-intercepts are;
The x-intercepts are;-1/3,2
Hence, the answer is the zeroes and x-intercepts are the same, they are;
[tex]-\frac{1}{3},2[/tex]Evaluate the expression when a=3 and b=6. b2-4a
Answers
b² - 4a
evaluated when a = 3 and b = 6 is:
6² - 4(3) =
= 36 - 12=
= 24
Boris's cat will be having four kittens. Boris performs asimulation by tossing a coin to model whether thesekittens will be male or female.• Let'heads (H) = female kitten• Let tails (T) = male kittenThe results of the simulation are:
Answers
Given:
Boris performs a simulation by tossing a coin to model whether these kittens will be male or female.
The total number of sample space is, N = 10.
Head for female kitten
T for male kitten.
The objective is to find the probability that at least three of the kittens will be male.
Fromthe obtained simulation, the number of sample space with at least thee tail (T) is, n(T)=4
Now, the probability of at least three of the kittens will be male can be calculated by,
[tex]undefined[/tex]Triangle DEF is rotated 60⁰ clockwise about the vertex to obtain triangle LMN. if the m
Answers
EXPLANATION
The measure of the angle LMN is equal to 40 degrees, then the measure of the angle LMN is the same because the rotation does not modify the angle.
f(x) = x^2 g(x) = x^2 - 8 g(x)= x^2 - 8 We can think of g as a translated (shifted) version of f. Complete the description of the transformation. Use nonnegative numbers. To get the function g, shift f [up/down/left/right] by [ ] units.
Answers
We have that the parent function (the original function is x^2). If we add a number after it as:
[tex]f(x)=x^2_{}+b[/tex]We affect the function in the y-axis, that is, we move the original function upward or downward.
Therefore, to get the function g, we need to shift the f function down by 8 units, that is
[tex]g(x)=f(x)-8=x^2-8[/tex]Question 10 of 12, Step 1 of 29/14CorrectConsider the following quadratic equation:3.x2 - 13x + 2 = -2Step 1 of 2: Using the standard form ax2 + bx + c = 0 of the given quadratic equation, factor theleft hand side of the equation into two linear factors.AnswerKeypadKeyboard Shortcuts= 0
Answers
Solution
- The question would like us to solve the quadratic equation:
[tex]3x^2-13x+2=-2[/tex]- The solution to this equation is given below:
[tex]\begin{gathered} 3x^2-13x+2=-2 \\ \text{Add 2 to both sides} \\ 3x^2-13x+4=0 \\ \\ \text{ We can rewrite the x-term as follows:} \\ -13x=-12x-x \\ \\ 3x^2-12x-x+4=0 \\ Let\text{ us factorize} \\ \\ 3x(x-4)-1(x-4)=0 \\ (x-4)\text{ is common } \\ \\ (x-4)(3x-1)=0 \end{gathered}[/tex]- Thus, the linear factors are
[tex]undefined[/tex]What are the slope and the y-intercept of the linear function that is represented by the table? -- Nicol у 3 2 1 0 -2 / 0 Nlw 3 1 2 -1 The slope is -3, and the y-intercept is 3 The slope is -3, and the y-intercept is z. 1 The slope is 3, and the v-intercept is -
Answers
We will assume the next table to answer this question (a linear function) (since the data in the question is not clear):
Having this information, we can find the slope using the formula for it:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]If we pick up from the table the next points:
x1 = 1, y1 =6
x2 = 2, y2 = 8
Then
[tex]m=\frac{8-6}{2-1}=\frac{2}{1}\Rightarrow m=2[/tex]We can use the slope-point formula to find the y-intercept. We can use the point (3, 10). Then, we have:
[tex]y-y_1=m\cdot(x-x_1)\Rightarrow y-10=2\cdot(x-3)\Rightarrow y-10=2x-6[/tex][tex]y=2x-6+10\Rightarrow y=2x+4[/tex]We end up with the slope-intercept formula for the line. Then the y-intercept is 4. In other words, if we have x = 0, then y = 4.
Then the slope for the values represented in the proposed table is m = 2, and the y-intercept is y = 4.
Find the axis of symmetry, vertex and which direction the graph opens, and the y-int for each quadratic function
Answers
Solution
Part a
The axis of symmetry
Part b
The vertex
Vertex (2,3)
Part c
The graph opens downward
Part D
The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0.
The y-intercept
[tex](0,-5)[/tex]Another
The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0.
[tex]\begin{gathered} y=-2x^2+8x-5 \\ y=-2(0)+8(0)-5 \\ y=0+0-5 \\ y=-5 \end{gathered}[/tex]x=0 y=-5
[tex](0,-5)[/tex]