Givn:
Value of the car in 1995 = $32,000
Value of the car in 2001 = $14,000
Let's solve for the following:
• (A). What was the annual rate of change between 1995 and 2001?
Apply the exponential decay formula:
[tex]f(t)=a(1-r)^t[/tex]Where:
• t is the number of years between 2001 and 1995 = 2001 - 1995 = 6
,• a is the initial value = $32000
,• r is the rate of decay.
,• f(t) is the present value
Thus, we have
[tex]\begin{gathered} 14000=32000(1-r)^6 \\ \end{gathered}[/tex]Divide both sides by 32000:
[tex]\begin{gathered} \frac{14000}{32000}=\frac{32000(1-r)^6}{32000} \\ \\ 0.4375=(1-r)^6 \end{gathered}[/tex]Take the 6th root of both sides:
[tex]\begin{gathered} \sqrt[6]{0.4375}=\sqrt[6]{(1-r)^6} \\ \\ 0.87129=1-r \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} r=1-0.87129 \\ \\ r=0.1287 \\ \\ r=0.1287*100=12.87\text{ \%} \end{gathered}[/tex]Therefore, the rate of change between 1995 and 2001 is 0.1287
• (B). What is the correct answer to part A written in percentage form?
In percentage form, the rate of change is 12.87 %
• (C),. Assume that the car value continues to drop by the same percentage. What will the value be in the year 2005?
We have the equation which represents this situation below:
[tex]f(t)=32000(1-0.1287)^t[/tex]Here, the value of t will be the number of years between 1995 and 2005.
t = 2005 - 1995 = 10
Now, substitute 10 for t and solve for f(10):
[tex]\begin{gathered} f(10)=32000(1-0.1287)^{10} \\ \\ f(10)=32000(0.8713)^{10} \\ \\ f(10)=32000(0.25216) \\ \\ f(10)=8069.14\approx8100 \end{gathered}[/tex]Therefore, the value in the year 2005 rounded to the nearest 50 dollars is $8100
ANSWER:
• (a). 0.1287
,• (b). 12.87%
,• (c). $8100
how many minutes until the heart beats 200 times
From the given table, we can read that the 200 beats is associated with the entry: "5 minutes", so that is the answer we pick.
which agrees with the first option in the provided list of possible answers.
Find the roots of the equation 5x2 + 125 = 0
The given equation is:
[tex]5x^2+125=0[/tex]Divide through by 5
[tex]\begin{gathered} \frac{5x^2}{5}+\frac{125}{5}=\frac{0}{5} \\ \\ x^2+25=0 \\ \end{gathered}[/tex]This is further simplified as:
[tex]\begin{gathered} x^2=-25 \\ \\ \sqrt{x^2}=\pm\sqrt{-25} \\ \\ \sqrt{x^2}=\pm\sqrt{-1}\times\sqrt{25} \\ \\ x^=\pm5i \\ \\ x=5i\text{ and -5i} \\ \end{gathered}[/tex]The graph of an inequality has a closed circle at 4.3, and the ray moves to the right. What inequality is graphed?x > 4.3x ≥ 4.3x ≤ 4.3x < 4.3
From the question, we were told that the graph of an inequality has a closed circle at 4.3 and the ray moves to the right also.
We are to determined the inequality that is graphed from the options.
From what is seen, we want x to be greater than or equal to 4.3.
The closed circle tells us that it can be equal to 4.3. The ray to the right tells us that we are looking for numbers larger than 4.3.
So the inequality graphed is that of x is greater than or equal to 4.3
So the correct option is the second option which is x ≥ 4.3.
Does the point (–48, –47) satisfy the equation y = x − 1?
To find the answer to the question, we will substitute "-48" into "x" and "-47" into "y" and see if the equation holds true or not.
[tex]\begin{gathered} y=x-1 \\ -47\stackrel{?}{=}-48-1 \\ -47\neq-49 \end{gathered}[/tex]Thus, the point (-48, -47) does not satisfy the equation y = x - 1.
AnswerNoFor which equation is x = 5 a solution ?
Given x = 5
We will find which equation will give a solution x = 5
1) x/2 = 10
so, x = 2 * 10 = 20
So, option (1) is wrong
2) x - 7 = 12
x = 12 + 7 = 19
So, option 2 is wrong
3) 2 + x = 3
x = 3 - 2 = 1
So, option 3 is wrong
4) 3x = 15
x = 15/3 = 5
So, the answer is option 3x = 15
write and slove six less then the product of a number n and 1/4 is no more than 96 fill in the boxs
ANSWER:
[tex]n\leq408[/tex]STEP-BY-STEP EXPLANATION:
With the statement we deduce the following inequality
[tex]\frac{1}{4}\cdot n-6\leq96[/tex]Solving for n
[tex]\begin{gathered} 4\cdot\frac{1}{4}\cdot n-4\cdot6\leq4\cdot96 \\ n-24\leq384 \\ n\leq384+24 \\ n\leq408 \end{gathered}[/tex]Question 2 - Minimum Hours f. In the previous question, if Leah babysits for 7 hours this month, what is the minimum number of hours she would have to work at the ice cream shop to earn at least $120? Justify your answer. (4 POINTS) Give your answer to the nearest whole hour.
Leah earns 5x + 8y dollars, after x hours babysitting and y hours at the ice cream shop.
She wants to earn at least $120, then:
5x + 8y ≥ 120
Given that Leah babysits for 7 hours, then:
5(7) + 8y ≥ 120
35 + 8y ≥ 120
8y ≥ 120 - 35
8y ≥ 85
y ≥ 85/8
y ≥ 10.625
She must work at least 11 hours
Given that 7 + 11 = 18, then she would not work more than 20 hours as she expected
what is 6q - q please
To solve this expression, we just have to subtract because they are like terms
[tex]6q-q=5q[/tex]Hence, the answer is 5q.
The ratio between the radius of the base and the height of a cylinder is 2:3. If it's volume is 1617cm^3, find the total surface area of the cylinder.
Solution:
The ratio of the radius to the height of the cylinder is
[tex]2\colon3[/tex]Let the radius be
[tex]r=2x[/tex]Let the height be
[tex]h=3x[/tex]The volume of the cylinder is given below as
[tex]V=1617cm^3[/tex]Concept:
The volume of a cylinder is given below as
[tex]V_{\text{cylinder}}=\pi\times r^2\times h[/tex]By substituting values, we will have
[tex]\begin{gathered} V_{\text{cylinder}}=\pi\times r^2\times h \\ 1617=\frac{22}{7}\times(2x)^2\times(3x) \\ 1617=\frac{22}{7}\times4x^2\times3x \\ 1617\times7=264x^3 \\ \text{divdie both sides by 264} \\ \frac{264x^3}{264}=\frac{1617\times7}{264} \\ x^3=\frac{343}{8} \\ x=\sqrt[3]{\frac{343}{8}} \\ x=\frac{7}{2} \end{gathered}[/tex]The radius therefore will be
[tex]\begin{gathered} r=2x=2\times\frac{7}{2} \\ r=7cm \end{gathered}[/tex]The height of the cylinder will be
[tex]\begin{gathered} h=3x=3\times\frac{7}{2} \\ h=\frac{21}{2}cm \end{gathered}[/tex]The formula for the total surface area of a cylinder is given below as
[tex]T\mathrm{}S\mathrm{}A=2\pi r(r+h)[/tex]By substituting the values, we will have
[tex]\begin{gathered} TSA=2\pi r(r+h) \\ TSA=2\times\frac{22}{7}\times7(7+\frac{21}{2}) \\ TSA=44(7+\frac{21}{2}) \\ TSA=44\times7+44\times\frac{21}{2} \\ TSA=308+462 \\ TSA=770cm^2 \end{gathered}[/tex]Hence,
The total surface area of the cylinder is = 770cm²
In 6-13 round each number to the place of the underlined digit
6. 32.7
7. 3.25
8. 41.1
9. 0.41
10. 6.1
11. 6.1
12. 184
13. 905.26
1) Considering that the underline marks the place to be rounded off we can do the following:
Note that if the number is greater than or equal to 5 then we will round it up.
If the number is lesser than 5 it will be rounded down.
Based on that we can round like this.
6. 32.7
7. 3.25
8. 41.1
9. 0.41
10. 6.1
11. 6.1
12. 184
13. 905.26
2)
Use your scatter plot of the temperature in 'n de in degrees North 2. The vertical intercept ans1°F The horizontal intercept ans2 °N
From the graph, the vertical intercept is 120°F
The slope, m, of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_!}[/tex]From the graph, the line passes through the points (0, 120) and (55, 60), then its slope is:
[tex]m=\frac{60-120}{55-0}=-\frac{12}{11}[/tex]The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept. In this case, the equation is
y = -12/11x + 120
Substituting with y = 0, we get:
[tex]\begin{gathered} 0=-\frac{12}{11}x+120 \\ -120=-\frac{12}{11}x \\ (-120)\cdot(-\frac{11}{12})=x \\ 110=x \end{gathered}[/tex]The horizontal intercept is 110°N
Solve for x: |x - 2| + 10 = 12 A x = 0 and x = 4B x = -4 and x = 0C x = -20 and x=4 D No solution
|x - 2| + 10 = 12
|x - 2| = 12 -10
|x - 2| = 2
There are 2 solutions:
x-2 = 2 and x-2 = -2
Solve each:
x = 2+2
x = 4
x-2=-2
x =-2+2
x=0
solution: x=0 and x = 4
Drag and drop the expressions into the boxes to correctly complete the proof of the polynomial identity.(x2 + y2)2 + 2x?y– y4 = x(x² + 4y?)(x2 + y2)2 + 2x²y2 – y4 = x(+ 4y?)+2x²y2 – y4 = x2 (x2 + 4y?)x² (x² + 47²)= x2 (x2 + 4y2)x² (x² + 47²) x² – 2x²y² + y x² + yt x² + 4x²72 x + 2x²,2x² + 2x²y² + yt
Answer:
x^4 + y^4 + 2x^2 y^2
x^4 + 4x^2y^2
x^2 (x^2 + 4y^2 )
Explanation:
Expanding the the expression gives
[tex]\begin{gathered} (x^2+y^2)^4=(x^2)^2+(y^2)^2+2(x^2)(y^2) \\ =\boxed{x^4+y^4+2x^2y^2\text{.}} \end{gathered}[/tex]Simplifying the Left-hand side gives
[tex]\begin{gathered} x^4+y^4+2x^2y^2+2x^2y^2-y^4 \\ =\boxed{x^4+4x^2y^2\text{.}} \end{gathered}[/tex]Finally, factoring out x^2 from the left-hand side gives
[tex]x^4+4x^2y^2=\boxed{x^2\mleft(x^2+4y^2\mright)\text{.}}[/tex]Question 25.Show if given 1-1 functions are inverse of each other. Graph both functions on the same set of axes and show the line Y=x as a dotted line on graph.
Given:
[tex]\begin{gathered} f(x)=3x+1_{} \\ g(x)=\frac{x-1}{3} \end{gathered}[/tex]To check the given functions are inverses of each other,
[tex]\begin{gathered} To\text{ prove: }f\mleft(g\mleft(x\mright)\mright)=x\text{ and g(f(x)=x} \\ f(g(x))=f(\frac{x-1}{3}) \\ =3(\frac{x-1}{3})+1 \\ =x-1+1 \\ =x \end{gathered}[/tex]And,
[tex]\begin{gathered} g(f(x))=g(3x+1) \\ =\frac{(3x+1)-1}{3} \\ =\frac{3x+1-1}{3} \\ =\frac{3x}{3} \\ =x \end{gathered}[/tex]It shows that, the given functions are inverses of each other.
The graph of the function is,
Blue line represents g(x)
Red line represents f(x)
green line represents y=x
The area of Square A is 36 square cm. The area of Square A’(A Prime) is 225 ᶜᵐ². What possible transformations did the square undergo?
A possible transformation is a scale. Since the area changed by
[tex]\frac{225}{36}=\frac{25}{4}[/tex]then a possible transformation was a scale by 25/4. A scale by a ratio bigger than one is a dilation.
Then the answer is B.
The senior classes at High School A and High School B planned separate trips to New York City.The senior class at High School A rented and filled 2 vans and 6 buses with 366 students. HighSchool B rented and filled 6 vans and 3 buses with 213 students. Each van and each bus carriedthe same number of students. Find the number of students in each van and in each bus.Answer: A van hasstudents and bus has students
Let V be the number of students that fit inside a van and B the number of students that fit inside a bus. Since 366 students fit in 2 vans and 6 buses, then:
[tex]2V+6B=366[/tex]Since 213 students fit in 6 vans and 3 buses, then:
[tex]6V+3B=213[/tex]Multiply the second equation by 2:
[tex]\begin{gathered} 2(6V+3B)=2(213) \\ \Rightarrow12V+6B=426 \end{gathered}[/tex]Then, we have the system:
[tex]\begin{gathered} 2V+6B=366 \\ 12V+6B=426 \end{gathered}[/tex]Substract the first equation from the second one and solve for V:
[tex]\begin{gathered} (12V+6B)-(2V+6B)=426-366 \\ \Rightarrow12V-2V+6B-6B=60 \\ \Rightarrow10V=60 \\ \Rightarrow V=\frac{60}{10} \\ \therefore V=6 \end{gathered}[/tex]Substitute V=6 into the first equation and solve for B:
[tex]\begin{gathered} 2V+6B=366 \\ \Rightarrow2(6)+6B=366 \\ \Rightarrow12+6B=366 \\ \Rightarrow6B=366-12 \\ \Rightarrow6B=354 \\ \Rightarrow B=\frac{354}{6} \\ \therefore B=59 \end{gathered}[/tex]Therefore, a van has 6 students and a bus has 59 students.
Perform a web search for images for the term graph of sales trends. Choose an image where there are both increasing and decreasing trends. Upload the image you found and discuss the time period(s) when the sales trend is increasing, and when it is decreasing. Also indicate any periods where the trend stayed constant (that is, it did not change).
Imagine you have a newsstand and you start to pay attention to how many magazines you sell each month for one year to understand which months you sell more and which months you sell less. So what you want is to understand the trends of your business.
So, after a year, you are able to draw a graph that represents all sales for this year per month as follows:
So, as we can see above, We have the sales of your newsstand from January to August. The x-axis indicates the months of the year and the y-axis indicate the number of magazines sold. We can see for January you sold 15 magazines and the number increased for February and Mars. Between Mars, April and May, it stayed constant and from May to August it decreased. It is represented by the line in red, where we have first an increasing trend, after a constant trend and finally a decreasing trend. So that is how it works, and now you can understand and explain how a graph of sales trends works and which kind of images you have to look for.
Find the exact area of la circle if its circumference is 367 cm.
Given the circumference to be 367 cm.
Recall that the formula for the circumference of a circle is given as;
[tex]\begin{gathered} C=2\pi r \\ \Rightarrow367=2\pi r \end{gathered}[/tex]If we make r the subject of the formula,
[tex]r=\frac{367}{2\pi}[/tex]The area of a circle is given as;
[tex]\begin{gathered} A=\pi r^2 \\ \Rightarrow\pi(\frac{367}{2\pi})^2=\frac{\pi}{4\pi^2}(367)^2=10718.21 \end{gathered}[/tex]1000=10 to the power 310,000= 10 to the power 4100,000=10 to the power 51,000,000= 10 to the power 6the next line is
According to the information, the question looks to construct the pattern given, at the left we can see that there is a 0 added in every line and at the right the exponent is added +1.
the next line in the pattern is
[tex]10,000,000=10^7[/tex]laws of exponent : multiplication and power to a poweranswer and help me step by step
All the numbers multiply in the normal way, and the powers of a power need to be multiplied.
[tex]72c^4d^8e^{10}[/tex]Let Iql = 5 at an angle of 45° and [r= 16 at an angle of 300°. What is 19-r|?13.00 14.2O 15.518.0
As given that:
[tex]|q|=5[/tex]At angle of45 degree
and |r| = 16 at 300 degree
so the |q| at 300 degree is:
[tex]\begin{gathered} |q|=5\times\frac{300}{45} \\ |q|=33.33 \end{gathered}[/tex]Now |q-r| is:
[tex]\begin{gathered} |q-r|=33.33-16 \\ |q-r|=17.33 \\ |q-r|\approx18 \end{gathered}[/tex]So the correct option is d.
having a bit of a problem with this logarithmic equation I will upload a photo
SOLUTION
We are asked to solve the equation
[tex]4^{5x-6}=44[/tex]44 cannot be written in index form. So to solve this, we will take logarithm of both sides of the equation
We will have
[tex]\log 4^{5x-6}=\log 44[/tex]Solving for x, we have
[tex]\begin{gathered} \log 4^{5x-6}=\log 44 \\ \\ 5x-6\log 4=\log 44 \\ \\ \text{dividing both sides by log4} \\ \\ 5x-6=\frac{\log 44}{\log 4} \\ \\ 5x=\frac{\log44}{\log4}+6 \end{gathered}[/tex]The exact solution becomes
[tex]x=\frac{(\frac{\log44}{\log4}+6)}{5}[/tex]The approximate solution to 4 d.p
[tex]\begin{gathered} x=\frac{(\frac{\log44}{\log4}+6)}{5} \\ \\ x=\frac{(\frac{1.64345}{0.60206}+6)}{5} \\ \\ x=\frac{8.72971}{5} \\ \\ x=1.7459 \end{gathered}[/tex]Each expression below represents the area of a rectangle written as a product tha area model for each expression on your paper and label its length and then we nation showing that the area written as a product is equal to the area wimen as the the parts de prepared to share your equations with the class. a. (x+3)(2x + 1) ca(224) d. (2x + 5)(x + y + 2) • (20 - 1999 (2x-1) (2x-1) g. 2(325) ( 2+ y + 3) 2
We have the expression:
[tex]x(2x-y)[/tex]It can be thougth as the area of a rectangle with sides x and (2x-y).
We can also think of the the difference between an area of a rectangle with sides x and 2x and a rectangle with sides x and y:
[tex]x(2x-y)=x\cdot2x-x\cdot y=2x^2-xy[/tex]Answer: x(2x-y) = 2x^2-xy
list all numbers from the given set that are
Part a
Natural numbers are:
[tex]\sqrt[]{25}[/tex]because
[tex]\sqrt[]{25}=5[/tex]Part b
whole numbers
[tex]0,\text{ }\sqrt[]{25}[/tex]Part c
Integers
[tex]-9,0,\sqrt[]{25}[/tex]Part d
rational numbers
[tex]\frac{3}{4},-9,0.6,0,8.5,\sqrt[]{25}[/tex]Part e
Irrational numbers
[tex]\pi,\text{ }-\sqrt[]{2}[/tex]Part f
real numbers
[tex]\frac{3}{4},-9,0.6,0,\pi,8.5,\sqrt[]{25},\text{ -}\sqrt[]{2}[/tex]For each value of w, determine whether it is a solution to w < 9.Is it a solution?W5?YesNo75914
Answer: 5 and 7
Explanation:
we need to determine if a number is a solution to
[tex]w<9[/tex]That reads as "w is less than 9, and not equal to 9"
so we find in our options wich ones are less than 9. The options are:
• 7
,• 5
,• 9
,• 14
The ones smaller or less than 9 are: 5 and 7
The ones greater than 9 or equal to 9 (the ones that are not the solution) are: 9 and 14.
So the solutions are: 5 and 7
In the first week of July, a record 1,040 people went to the local swimming pool. In the second week,125 fewer people went to the pool than in the first week. In the third week,135 more people went to the pool than in the second week. In the fourth week,322 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
By the concept of percentage there is 20% decrease in the number of people who went to the pool over these four weeks.
What is percentage?A percentage is a statistic or ratio that is expressed as a fraction of 100 in mathematics. But even though the abbreviation "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to signify it. A % is a dimensionless number; there is no specific unit of measurement for it. %, a relative figure signifying hundredths of any amount. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. A percentage is a figure or ratio that in mathematics represents a portion of one hundred. It is frequently represented by the sign "%" or just "percent" or "pct." For instance, the fraction or decimal 0.35 is comparable to 35%.
In July:
First week:
Number of people went to the local swimming pool
=1040
Second week:
110 fewer people went to the pool than in the first week
Number of people went to the local swimming pool
=1040 - 110
=930
Third week:
130 more people went to the pool than in the second week
Number of people went to the local swimming pool
=930 + 130
=1060
Fourth week:
228 fewer people went to the pool than in the third week
Number of people went to the local swimming pool
=1060 - 228
=832
Decrease in number of people over four week
= number of people in first week - number of people in fourth week
Decrease in number of people over four week
=1040 - 832
=208
Now, the percentage
= 20%
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1.For a standard normal distribution, find:P(1.26 < z < 1.48)2.For a standard normal distribution, given:P(z < c) = 0.1288
Standard Normal Distribution
To find the cumulative probability of a Normal Distribution, we need to use some automated digital tool that makes the calculations for us, since it's a pretty complex formula.
We'll use an online tool and provide the results here.
a) P(1.26 < z < 1.48)
The procedure is: Find P(z < 1.48) directly from the tool. Find P(z < 1.48) also. Subtract both values.
P(z < 1.48) = 0.931
P(z < 1.26) = 0.896
Subtract the values above: 0.931 - 0.896 = 0.035. Thus:
P(1.26 < z < 1.48) = 0.035
b) Find c such that: P(z < c) = 0.1288
We need to use the inverse Normal Distribution, enter the probability and find the z-score: c = -1.132
It took Carmen 4 hours to drive 200 miles. Using context clues from the problem, what formula can be used to find George's rate of speed?
From the information given, we can find th rate of speed with the equation;
[tex]\text{distance = rate x time}[/tex]Or;
[tex]d=rt[/tex]Go step by step to reduce the radical. V 243 DVD try You must answer all questions above in order to submit.
We are given the following radical
[tex]\sqrt[]{243}[/tex]Let us reduce the above radical
We need to break the number 243 into a product of factors
Notice that 81 and 3 are the factors (83×3 = 243)
[tex]\sqrt[]{243}=\sqrt[]{81}\cdot\sqrt[]{3}[/tex]Since 81 is a perfect square so the radical becomes
[tex]\sqrt[]{243}=\sqrt[]{81}\cdot\sqrt[]{3}=9\cdot\sqrt[]{3}[/tex]Therefore, the simplified radical is
[tex]undefined[/tex]Find the z-score location of a vertical line that separates anormal distribution as described in each of the following.a. 15% in the tail on the rightb. 40% in the tail on the leftc. 75% in the body on the rightd. 60% in the body on the left
Answer:
a. z = 1.0364
b. z = -0.2533
c. z = -0.6745
d. z = 0.2533
Explanation:
We can represent each option with the following diagrams
So, for each option, we need to find a z that satisfies the following
a. P(Z > z) = 0.15
b. P(Z < z) = 0.40
c. P(Z > z) = 0.75
d. P(Z > z) = 0.60
Then, using a normal table distribution, we get that each value of z is
a. z = 1.0364
b. z = -0.2533
c. z = -0.6745
d. z = 0.2533