Solution
For this case we can use the following formula:
[tex]A=Pe^{rt}^{}[/tex]and for this case we have the following:
P= 12600
A= 7100
t = 9 years
And r is the value that we need to find, so we can do the following:
[tex]12600=7100e^{9r}[/tex]We can do the following:
[tex]\ln (\frac{12600}{7100})=9r[/tex]And we got for r:
[tex]r=\frac{\ln (\frac{12600}{7100})}{9}=0.0637[/tex]And then the rate would be:
6.37%
Question 8 of 10If f(x) = - VX-3, complete the following statement (round your answerto the nearest hundredth):3x + 2f(7) = —Answer hereSUBMITplease help
To find f(7) substitute x by 7 in the function
Describe the complement of the given event. 73% of nineteen year old males are at least 166 pounds
Solution
- The event is "73% of nineteen year old males are at least 166 pounds"
- The complement of this event is the set of all 19 year old males not in the event described above.
- These set of 19 year olds, must represent the remaining 27% of the population.
- Also, they would weigh less than 166 pounds.
- Thus, the complement of the event is:
"27% of nineteen year old males weigh less than 166 pounds"
Find the equation of the line that is parallel to the line y = -2x +3 and passes through the point (5,4).y = − 1/2x + 6.5y = 2x - 14y = -2x + 14y = 1/2x + 1.5
lets remember how to find the equation of a parallel line
two lines are parallel if they don"t intersect, that means they slopes are the same
y=-2x+3
slope as we see is m=-2
the other line has to pass through point (5,4)
y-y1=m(x-x1)
y-4=-2(x-5)
we solve the equation
y= 4-2x+10
y= -2x+14
i will send you a picture
green line is y=-2x+14
Laura needs summer blouses. She bought 1 blouseand 2 sweaters. How much did she spend? Did shebuy clothes that matched her summer needs?
Given:-
Cost of blouse is $27.50
Cost of sweater is $34.99
To find the cost if laura bought :-
So since laura bought one blouse and two sweaters, we get
[tex]27.50+2(34.99)=97.48[/tex]So the cost is $97.48 and she bought the cloths of her summer needs.
Question 5 Fill in the table. First Integer Next Integers Give four consecutive odd integers: The simplified sum of the second and forth integers are Question Help: Message instructor Submit Question
The four consecutive odd integers
If the first integer is given to be x
Then the next three are:
x + 2, x+ 4 and x+ 6
The sum of the second and forth integers :
x+2 + x+ 6 = 2x + 8
Hence, the sum of the second and forth integers are: 2x+8
find the slop of the line passing through the points (1,-1) and (-1,1)
Answer:
I think its done this way. But I don't know if the answer is correct.
8. Three consecutive even numbers have a sum where one half of that sum is between 90 and 105. a. Write an inequality to find the three numbers. Let n represent the smallest even number. b. Solve the inequality. a. (n+(n+2)+(n+4) < −90 or −(n+(n+2)+(n+4)) > 105 b. n-62 or n > 68 a. 90 < 2(n + (n + 2) + (n + 4)) < 105 b. 13 ≤ n ≤ 15.5 a. 90 < ¹² (n + (n +2)+(n+ 4))
Given:
Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.
Required:
To write an inequality to find the three numbers and to solve the inequality.
Explanation:
(a)
Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.
[tex]90<\frac{1}{2}(n+(n+2)+(n+4))<105[/tex](b)
[tex]undefined[/tex]a scuba diver descended 19 5/12 feet blow sea level. Then he descended another 3 3/5 feet. Which of the following is true about the scuba diver after both descents?
The position of the scuba diver is 23 1/60 feet.
How to calculate the fraction?From the information, the scuba diver descended 19 5/12 feet blow sea level and then he descended another 3 3/5 feet.
The position of the diver will be. the addition of the fraction for descending. This will be:
= 19 5/12 + 3 3/5
= 19 25/60 + 3 36/60
= 22 61/60
= 23 1/60
Note that your information is incomplete as the question was answered based on information given.
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NO LINKS!! Please help me with this probability question 2a
====================================================
Work Shown:
A = he eats pizza
B = he drinks cola
P(A) = 0.40
P(B) = 0.60
P(A and B) = 0.30
Then apply the conditional probability formula.
P(A given B) = P(A and B)/P(B)
P(A given B) = 0.30/0.60
P(A given B) = 0.5 exactly
P(A given B) = 50%
If we know for certain he drinks cola, then there's a 50% chance of him eating pizza.
Which system of equations best represents the situation below?A farmer grew his own tomatoes (a), eggplants (b), and potatoes (c). Hedecided to package his vegetables and price them as follows:1 tomato, 1 eggplant, 2 potatoes for $102 tomatoes, 1 eggplant, 3 potatoes for $144 tomatoes, 3 eggplants, 5 potatoes for $20
Solution
- The cost of the crops are $(a) for tomatoes, $(b) for eggplants, and $(c) for potatoes.
- We simply need to follow the statements about the farmer's pricing in order to determine the correct set of equations.
Statement 1:
- "1 tomato, 1 eggplant, 2 potatoes for $10"
- If there is 1 tomato, it implies that, this tomato is priced at $(a). Similarly, 1 eggplant would be priced at $(b), but 2 potatoes would be $(c) + $(c) = $2(c).
- We are told that the total cost for this package is $10.
- Thus, the first equation must be:
[tex]a+b+2c=10[/tex]- We can interprete the other packages in a similar manner.
Statement 2:
"2 tomatoes, 1 eggplant, 3 potatoes for $14"
- This implies that the farmer would price the packages as follows:
2 tomatoes: 2(a)
1 eggplant: 1(b)
3 potatoes: 3(c)
- Since the total cost is $14, we can write the second equation as follows:
[tex]2a+b+3c=14[/tex]Statement 3:
"4 tomatoes, 3 eggplants, 5 potatoes for $20"
- This implies that the farmer would price the packages as follows:
4 tomatoes: 4(a)
3 eggplants: 3(b)
5 potatoes: 5(c)
- Since the total cost is $20, we can write the third equation as follows:
[tex]4a+3b+5c=20[/tex]Final Answer
The 3 equations are:
[tex]\begin{gathered} a+b+2c=10 \\ 2a+b+3c=14 \\ 4a+3b+5c=20 \end{gathered}[/tex]OPTION C
how many inches are in 20 centimeters?
We know that an inch is equivalent to 2.54 centimeters, then if we want to know how many inches are in a centimeters we do this:
[tex]a\times\frac{1inch}{2.54\operatorname{cm}}[/tex]In this case, we have 20 centimeters, then replacing a by 20 we find the equivalent inches to 20 like this:
[tex]20\text{cm}\times\frac{1inch}{2.54\operatorname{cm}}\approx7.87\text{inches}[/tex]Which of the following tables shows a uniform probability model?
The answer is the third choice
Where all probability are equal
I would like to learn the long multiplication so I can teach my fifth grader this math problem
352x20=
Answer: 7040
Step-by-step explanation:
1
352
x20
——-
000
7040
+
———
7040
PLS HELP Quadrilateral ABCD is located at A(-2, 2), B(-2, 4), C(2, 4), and D(2, 2). The quadrilateral is then transformed using the rule (x + 7, y - 1) to form the imagecoordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments
Given:
The coordinates of Quadrilateral ABCD is A(-2, 2), B(-2, 4), C(2, 4), and D(2, 2).
The quadrilateral is transformed with the rule,
[tex](x,y)\rightarrow\mleft(x+7,y-1\mright)[/tex]It becomes,
[tex]\begin{gathered} A\mleft(-2,2\mright)\rightarrow A^{\prime}\mleft(-2+7,2-1\mright)=A^{\prime}(5,1) \\ B\mleft(-2,4\mright)\rightarrow B^{\prime}(-2+7,4-1)=B^{\prime}(5,3) \\ C\mleft(2,4\mright)\rightarrow C^{\prime}(2+7,4-1)=C^{\prime}(9,3) \\ D(2,2)\rightarrow D^{\prime}(2+7,2-1)=D^{\prime}(9,1) \end{gathered}[/tex]Now, join the corresponding vertices of both the quadrilateral with the line segment.
After joining the vertices of the quadrilateral ABCD and A'B'C'D'. it gives the 3-dimensional shape- a rectangular prism.
find the first second and third derivatives of the function
Given the function
[tex]f(x)=\frac{8}{5}x-9[/tex]Finding the derivative we have
[tex]f^{^{\prime}}(x)=\frac{8}{5}[/tex]Also
[tex]f^{\doubleprime}(x)=0^{}[/tex]Finally
[tex]f^{^{\doubleprime}^{\prime}}(x)=0[/tex]Question 8 Let h(t) = –1612 +64 + 80 represent the height of an object
To find the time it takes the object to reach the maximum height we need to remember that this happens in the axis of symmetry of the parabola described by the function:
[tex]h(t)=at^2+bt+c[/tex]The axis of symmetry is given as:
[tex]t=-\frac{b}{2a}[/tex]in this case we have that a=-16 and b=64, then we have:
[tex]t=-\frac{64}{2(-16)}=\frac{-64}{-32}=2[/tex]Therefore it takes 2 seconds to the object to reach its maximum height.
Now, to find the maximum height we plug this value of t in the equation, then we have:
[tex]\begin{gathered} h(2)=-16(2)^2+64(2)+80 \\ =-16(4)+128+80 \\ =-64+128+80 \\ =144 \end{gathered}[/tex]therefore the maximum height is 144 ft.
12x÷4yif x=-8 and y=3
To solve 12x÷4y, first, let's evaluate the products on both sides of the ÷ symbol, we know that x = -8, then we have:
[tex]12\times(-8)=-96[/tex]We have -96 on the left side of the ÷ symbol.
We know that y = 3, then, on the right side, we have:
[tex]4\times3=12[/tex]Then, we have 12 on the right side of the ÷ symbol, now the expression looks like this:
-96 ÷ 12. what we have to do is to divide -96 by 12, then we get:
[tex]-96\text{ }\div12=\frac{-96}{12}=-8[/tex]Then, the answer is 8
3. Suppose an investment of $5000 doubles every 12 years. How much is the investment worth after: 24 years?
Money = $5000
time = 12 years
investment after 24 years
If the investment doubles every 12 years after 24 years the total amount of money will be $10000.0
On the desmos app can you have more standard forms or only one?
Answer: I am pretty sure you can only have one.
Step-by-step explanation:
Find the 11th term of the arithmetic sequence -5x- 1, -8x + 4, -11 x+ 9, ...
Recall that an arithmetic sequence is a sequence in which the next term is obtained by adding a constant term to the previous one. Let us consider a1 = -5x-1 as the first term and let d be the constant term that is added to get the next term of the sequence. Using this, we get that
[tex]a_2=a_1+d[/tex]so if we replace the values, we get that
[tex]-8x+4=-5x-1+d[/tex]so, by adding 5x+1 on both sides, we get
[tex]d=-8x+4+5x+1\text{ =(-8+5)x+5=-3x+5}[/tex]To check if this value of d is correct, lets add d to a2. We should get a3.
Note that
[tex]a_2+d=-8x+4+(-3x+5)=-11x+9=a_3[/tex]so the value of d is indeed correct.
Now, note the following
[tex]a_3=a_2+d=(a_1+d)+d=a_1+2d=a_1+d\cdot(3-1)[/tex]This suggest the following formula
[tex]a_n=a_1+d\cdot(n-1)[/tex]the question is asking for the 11th term of the sequence, that is, to replace the value of n=11 in this equation, so we get
[tex]a_{11}=a_1+d\cdot(10)=-5x-1+10\cdot(-3x+5)\text{ =-5x-1-30x+50 = -35x+49}[/tex]so the 11th term of the sequence is -35x+49
Rewrite the equation in Ax+By=C form.Use integers for A, B, and C.y-4=-5(x+1)
The given equation is
[tex]y-4=5(x+1)[/tex]To write the equation in standard form, first, we have to use the distributive property.
[tex]y-4=5x+5[/tex]Now, we subtract 5x and 5 on both sides.
[tex]\begin{gathered} y-4-5x-5=5x+5-5x-5 \\ -5x+y-9=0 \end{gathered}[/tex]Now, we add 9 on each side
[tex]\begin{gathered} -5x+y-9+9=0+9 \\ -5x+y=9 \end{gathered}[/tex]Therefore, the standard form of the given equation is[tex]-5x+y=9[/tex]Where A = -5, B = 1, and C = 9.Determine the perimeter of this shape. Use 3.14 for pi. the numbers are 12m and 15 m
We are asked to find the perimeter of the figure. To do that we will add the perimeters of the semi-circle and the rectangle.
To determine the perimeter of the semi-circle we will use the following formula:
[tex]P_{c\text{ }}=\frac{\pi D}{2}[/tex]The diameter is 12 m. Replacing in the formula we get:
[tex]P_c=\frac{\pi(12m)}{2}[/tex]Solving the operations:
[tex]P_c=\frac{3.14(12)}{2}=6.28m[/tex]Now we will find the perimeter of the rectangle by adding the length of all of its sides:
[tex]P_R=15m+12m+15m=42m[/tex]Now, the perimeter of the figure is the sum of the perimeters we found:
[tex]\begin{gathered} P=P_c+P_R \\ \end{gathered}[/tex]Replacing:
[tex]P=6.28m+42m=48.28m[/tex]Therefore, the perimeter of the figure is 48.28m
Which points are separated by a distance of 4 units?A. (3,6) (3,9)B. (2,7) (2,3)C. (1,5) (1,3)D. (4,2) (4,7)
let us take the point (2,7) and (2,3) the distance between these two is
[tex]\begin{gathered} d=\sqrt[]{(2-2)^2+(7-3)^2} \\ d=\sqrt[]{4^2} \\ d=4\text{ unit} \end{gathered}[/tex]Hence these two points are separated by 4 units.
So option B is correct.
Write the decimal as a quotient of two integers in reduced form.
0.513
The given decimal can be written as a quotient of 513/1000.
What is quotient?
In maths, the result of dividing a number by any divisor is known as the quotient. It refers to how many times the dividend contains the divisor. The statement of division, which identifies the dividend, quotient, and divisor, is shown in the accompanying figure. The dividend 12 contains the divisor 2 six times. The quotient is always less than the dividend, whether it is larger or smaller than the divisor.
we can write the decimal given 0.513 as a answer of of 513 divided by 1000.
I.e.
[tex]0.513 = \frac{513}{1000}[/tex]
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The floor of a shed has an area of 80 square feet. The floor is in the shape of a rectangle whose length is 6 feet less than twice the width. Find the length and the width of the floor of the shed. use the formula, area= length× width The width of the floor of the shed is____ ft.
Given:
The area of the rectangular floor is, A = 8- square feet.
The length of the rectangular floor is 6 feet less than twice the width.
The objective is to find the measure of length and breadth of the floor.
Consider the width of the rectangular floor as w, then twice the width is 2w.
Since, the length is given as 6 feet less than twice the width. The length can be represented as,
[tex]l=2w-6[/tex]The general formula of area of a rectangle is,
[tex]A=l\times w[/tex]By substituting the values of length l and width w, we get,
[tex]\begin{gathered} 80=(2w-6)\times w \\ 80=2w^2-6w \\ 2w^2-6w-80=0 \end{gathered}[/tex]On factorizinng the above equation,
[tex]\begin{gathered} 2w^2-16w+10w-80=0 \\ 2w(w-8)+10(w-8)=0 \\ (2w+10)(w-8)=0 \end{gathered}[/tex]On solving the above equation,
[tex]\begin{gathered} 2w+10=0 \\ 2w=-10 \\ w=\frac{-10}{2} \\ w=-5 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} w-8=0 \\ w=8 \end{gathered}[/tex]Since, the magnitude of a side cannot be negative. So take the value of width of the rectangle as 8 feet.
Substitute the value of w in area formula to find length l.
[tex]\begin{gathered} A=l\times w \\ 80=l\times8 \\ l=\frac{80}{8} \\ l=10\text{ f}eet. \end{gathered}[/tex]Hence, the width of the floor of the shed is 8 ft.
6. Express the given function h as a composition of two functions f and g
such that H(x) = (fog)(x).
a) H(x) = |3x +2|
b) H(x) = √√√√5x +4
The given function can be represented f(x) and g(x) as below
What are functions?
A function from X to Y is an assign of each constituent of Y to each variable of X. The set X is known as the function's scope, while the set Y is known as the function's image domain. The notation f: XY denotes a function, its domain, and its codomain, and the value of a function f at an element x of X, indicated by f(x), is known as the image of x under f, or the value of f applied to the argument x. When defining a function, the domains and codomain are not often explicitly specified, and without performing some (complicated) calculation, one may only know that perhaps the domain is included in a larger package.
The functions are
(a) f(x) = 3x+2 and g(x) = |x|
so, H(x) = f(g(x)) = |3x+2|
(b) f(x) = 5x+4 and g(x) = √√√√x
so, H(x) = f(g(x)) = √√√√5x+4
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if the author sells x Books per day his profit will be : J(X)= (-0.001x^2)+3x-1800Find the max profit per dayFind the amount of books the author must sell for the most profit
The given function in a quadratic function in standard form where
a = -0.001, b = 3, and c = -1800
It is a parabola that is facing downwards, therefore, the vertex of this parabola, (x,y) is the maximum of the function where
x is the amount of books that the author must sell for the most profit, and
y is the max profit per day.
We can find the vertex using
[tex]x=\frac{-b}{2a}[/tex]Substitute the following values, and we get
[tex]\begin{gathered} x=\frac{-b}{2a} \\ x=\frac{-3}{2(-0.001)} \\ x=\frac{-3}{-0.002} \\ x=1500 \end{gathered}[/tex]Now that we have x, plug it in the original function to solve for y
[tex]\begin{gathered} J(x)=\mleft(-0.001x^2\mright)+3x-1800 \\ J(1500)=-0.001(1500)^2_{}+3(1500)-1800 \\ J(1500)=-2250+4500-1800 \\ J(1500)=450 \end{gathered}[/tex]We have determine that the vertex of the function is at (1500,450). We can now conclude that
The max profit per day is $450.
The amount of of books the author must sell for the most profit is 1500 books.
A growing number of thieves are using keylogging programs to steal passwords and other personal information from Internet users. The number of keyloggingprograms reported grew approximately exponentially from 0.3 thousand programs in 2001 to 11.0 thousand programs in 2008. Predict the number of keyloggingprograms that will be reported in 2013
Exponential growth (EG):
2001 = 0.3
2008 = 11
2013 = ?
[tex]n\text{ = }a\times b^t[/tex]a = initial amount = 0.3
b= growth factor = ?
t = period = 7
n = 11
[tex]\begin{gathered} 11=0.3\times b^7 \\ b^7=\frac{11}{0.3} \\ b\text{ = }\sqrt[7]{\frac{11}{0.3}} \\ b=1.67 \end{gathered}[/tex]b = 1.67
Solving the number of keylogging programs that will be reported in 2013:
[tex]\begin{gathered} n\text{ = }0.3\times1.67^{12} \\ n=144.12 \end{gathered}[/tex]Write an equation of the line passing through the point (8,-3) that is parallel to the line y= -x -1. An equation of the line is
The equation of the line, in slope-intercept form, that is parallel to the line y = -x - 1 is: y = -x + 5.
How to Write the Equation of Parallel Lines?Parallel lines have equal slope value, "m". In slope-intercept form, the equation y = mx + b represents a line, where the slope is "m" and the y-intercept is "b".
The slope of y= -x -1 is -1. This means the line that is parallel to y= -x -1 will also have a slope that is equal to -1.
Substitute m = -1 and (x, y) = (8, -3) into y = mx + b to find the value of b:
-3 = -1(8) + b
-3 = -8 + b
-3 + 8 = b
5 = b
b = 5
Substitute b = 5 and m = -1 into y = mx + b to wrote the equation of the line that is parallel y = -x -1:
y = -x + 5
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Find the x - and y -intercepts of the graph of the linear equation -6x + 9y = -18
Someone else got x=(3,0) y=(0,-2) but it was wrong
Answer:
x-intercept = 3y-intercept = -2Step-by-step explanation:
You want the intercepts of the equation -6x +9y = -18.
InterceptsThere are several ways to find the intercepts. In each case, the x-intercept is the value of x that satisfies the equation when y=0, and vice versa.
For y = 0, we find the x-intercept to be ...
-6x + 0 = -18
x = -18/-6 = 3
The x-intercept is 3; the point at that intercept is (3, 0).
For x = 0, we find the y-intercept to be ...
0 +9y = -18
y = -18/9 = -2
The y-intercept is -2; the point at that intercept is (0, -2).
Intercept formThe intercept form of the equation for a line is ...
x/a +y/b = 1
where 'a' is the x-intercept, and 'b' is the y-intercept.
We can get this form by dividing the original equation by -18.
-6x/-18 +9y/-18 = 1
x/3 +y/(-2) = 1
The x-intercept is 3; the y-intercept is -2.
__
Additional comment
When asked for the intercepts, it is sometimes not clear whether you are being asked for the value where the curve crosses the axis, or whether you are being asked for the coordinates of the point there.
Your previous "wrong" answer was given as point coordinates. Apparently, just the value at the axis crossing is required.
You have to have some understanding of your answer-entry and answer-checking software to tell the required form of the answer (or you can ask your teacher).
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