Step 1
Given; The population of the county, which follows the exponential growth model,
increased from 491,675 in 2000 to 782,341 in 2010.
Write the exponential growth function.
Step 2
The exponential function is given as;
[tex][/tex]Suppose that there are two types of tickets to a show: advance and same day. Advance tickets cost 30 and the same day tickets cost 20. For one performance there were 60 tickets sold in all and the total amount paid for them was $1600. How many tickets of each type were sold
Let A be the number of advance tickets sold and S be the total number of same-day tickets sold. The total amount of tickets is A+S, then:
[tex]A+S=60[/tex]The total earnings for A advanced tickets is 30A, while the total earnings for selling S same-day tickets is 20S. Then, the total amount of money for selling A advanced tickets and S same-day tickets, is 30A+20S, then:
[tex]30A+20S=1600[/tex]Solve the system of equations to find the total amount of tickets of each type that were sold. To do so, isolate A from the first equation and then substitute the resulting expression in the second one:
[tex]\begin{gathered} A+S=60 \\ \Rightarrow A=60-S \end{gathered}[/tex][tex]\begin{gathered} 30A+20S=1600 \\ \Rightarrow30(60-S)+20S=1600 \end{gathered}[/tex]Solve for S:
[tex]\begin{gathered} \Rightarrow1800-30S+20S=1600 \\ \Rightarrow1800-10S=1600 \\ \Rightarrow-10S=1600-1800 \\ \Rightarrow-10S=-200 \\ \Rightarrow S=-\frac{200}{-10} \\ \therefore S=20 \end{gathered}[/tex]Substitute S=20 into the expression for A:
[tex]\begin{gathered} A=60-S \\ =60-20 \\ =40 \end{gathered}[/tex]Then, the solution for this system is:
[tex]\begin{gathered} A=40 \\ S=20 \end{gathered}[/tex]What does 10 represent in 10/6
10/6
This is a fraction, in a fraction the bottom number represents the denominator and the top number represents the numerator.
So, in this case, 10 represents the numerator.
Is the area of a semicircle with a diameter of x greater than, less than, or equal to the area of a circle with a diameter of 1/2x? Explain
Since area of semi-circle=[tex]\pi[/tex].x²/8 and area of circle=[tex]\pi[/tex]x²/16 we can conclude that area of semi-circle with a diameter of x is greater than circle with a diameter of 1/2x.
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.
What is circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
Here,
Area of a semicircle with a diameter of x and a circle with a diameter of 1/2x.
area of semi-circle=1/2( [tex]\pi[/tex]r²)
2r=x
r=x/2
=1/2[tex]\pi[/tex].x²/4
area of semi-circle=[tex]\pi[/tex].x²/8
area of circle= [tex]\pi[/tex]r²
2r=d
d=1/2x
r=1/4x
=[tex]\pi[/tex].(x/4)²
area of circle=[tex]\pi[/tex]x²/16
We can infer that a semicircle with a diameter of x has a larger area than a circle with a diameter of 1/2x because the area of a semicircle is equal to π.x²/8 and the area of a circle is equal to πx²/16.
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3450 turns to degrees and 3450 turns to radians.
We will have the following:
*First: We know that 1 turn will be equal to 360°. So:
[tex]3450\cdot360=1242000[/tex]So, 3450 turns equal to 1 242 000 degrees.
*Second: We have that the expression to convert degrees to radians is:
[tex]d\cdot\frac{\pi}{180}=r[/tex]Here d represents degrees and r radians. So, we replace the number of degrees and solve for radians:
[tex](1242000)\cdot\frac{\pi}{180}=6900\pi[/tex]So, 3450 turns are 6900pi radians.
calculate the surface area of a hollow cylinder which is closed at one end if the base radius is 3.5 cm and the height is 8 cm
Answer:
A=2πrh+2πr2=2·π·3.5·8+2·π·3.52≈252.89821cm²
The surface area is 214.305cm².
What is surface area?The surface area is the area of the outer covering of the object.
It is given that radius, r=3.5 cm, and height, h=8 cm.
The surface area of the given object will be the sum of curved surface area and the area of the bottom, which is circle.
Surface Area = Curved Surface Area + Area of bottom circle
=2πrh+πr²
=2π(3.5)(8)+π(3.5)²
=56π+12.25π
=68.25π
Substitute π=3.14 to determine the surface area.
Surface Area = 68.25(3.14)
=214.305
So, the surface area will be 214.305cm².
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Rewrite the following equation in slope-intercept form. x - 7y = 20 Write your answer using integers, proper fractions, and improper fractions in simplest form.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
x - 7y = 20
slope-intercept form = ?
Step 02:
Slope-intercept form of the line
y = mx + b
x - 7y = 20
x = 20 + 7y
x - 20 = 7y
7y = x - 20
[tex]y\text{ = }\frac{x}{7}\text{ - }\frac{20}{7}[/tex]The answer is:
y = x/7 - 20/7
What are the solutions to the equation (x-3)(x+5)=-15
Hence, the solutions of the equation is [tex]x = 0, -2[/tex].
What is the equation?
A mathematical statement that shows that two mathematical expressions are equal.
Here given expression is
[tex](x-3)(x+5)=-15\\\\x^2+5x-3x-15=-15\\\\x^2+5x-3x=0\\\\x^2+2x=0\\\\x(x+2)=0\\\\x=0,-2[/tex]
Hence, the solutions of the equation is [tex]x = 0, -2[/tex].
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Jenny borrowed $8000 at a rate of 9%, compounded semiannually. Assuming she makes no payments, how much will she owe after 10Do not round any intermediate computations, and round your answer to the nearest cent.
SOLUTION
We will use the formula
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ where\text{ } \\ A=amount\text{ after 10 years = ?} \\ P=money\text{ borrowed = \$8,000} \\ r=9\%=\frac{9}{100}=0.09 \\ t=time\text{ in years = 10} \\ n=compounding=semi-annualy=2 \end{gathered}[/tex]plugging in, we have
[tex]\begin{gathered} A=8,000(1+\frac{0.09}{2})^{2\times10} \\ A=8,000(1.045)^{20} \\ A=8,000\times2.4117140 \\ A=19,293.7121986 \end{gathered}[/tex]Hence the answer is $19,293.71
Which of the following sets does the number 12 over five belong to
The given figure is
12/5 = 2.4
Firstly, let us define the terms.
whole numbers are set of natural number including zero. It does not include decimals. Thus, 12/5 is not a whole number
Integers are are the set of whole numbers including all the negative natural numbers. It does not include fractions. Thus, 12/5 is not a whole number
Rational numbers is a set of fractions where the denominators and numerators are integers. Since 5 and 12 are integers, 12/5 is a rational number
Irrational numbers are numbers that numbers that cannot be written on the number line. They include square root of 2, pi. etc. Thus, 12/5 is not an irrational number
Real numbers is the set of all rational and irrational numbers. Thus, 12/5 is a real number
Therefore, the correct options are
please show work on how to get the points we graph
Answer:
Graphing the inequalities, we have;
Explanation:
Given the system of quadratic inequalities;
[tex]\begin{cases}y<-x^2-x+8 \\ y>x^2+2\end{cases}[/tex]Graphing the quadratic inequalities;
for the first quadratic inequality;
[tex]\begin{gathered} y<-x^2-x+8 \\ at\text{ x=0} \\ y<8 \\ (0,8) \\ at\text{ x=-0.5} \\ y<-(-0.5)^2-(-0.5)+8 \\ y<8.25 \\ (-0.5,8.25) \\ at\text{ x=-2} \\ y<-(-2)^2-(-2)+8 \\ y<-4+2+8 \\ y<6 \\ (-2,6) \\ at\text{ x=}2 \\ y<-(2)^2-(2)+8 \\ y<-4^{}-2+8 \\ y<2 \\ (2,2) \end{gathered}[/tex]For the second quadratic inequality;
[tex]\begin{gathered} y>x^2+2 \\ at\text{ x=0} \\ y>2 \\ at\text{ x=2} \\ y>(2)^2+2 \\ y>6 \\ (2,6) \\ at\text{ x=-2} \\ y>(-2)^2+2 \\ y>6 \\ (-2,6) \end{gathered}[/tex]Graphing the two inequalities using the points derived above.
Note that both inequalities would be dashed lines because of the inequality sign, and the shaded part will be according to the sign.
Graphing the inequalities, we have;
determine the point and slope that were used to write each linear equation in point slope form
The slope-point form is:
[tex]y-y_0=m(x-x_0)[/tex]where (x0,y0) is a point in the line and m is the slope.
A) If the equation is written in slope-point form, we have:
[tex]y-0=2(x-5)[/tex]Then, the point is (5,0) and the slope is m=2.
Answer: Point = (5,0)
Slope = 2
B)
[tex]\begin{gathered} y+3=5x \\ y-(-3)=5(x-0) \end{gathered}[/tex]Answer: Point (0,-3)
Slope = 5
Please help me and explain to me these questions step by step. Thank youQuestion 8: Use simple interest
Given:
Amount Nicole borrowed = $1100
Annual interest rate = 7%
Duration = 6 months
Let the amount of interest be x
The amount after t years can be calculated using the formula:
[tex]\text{Amount = }P(1\text{ }+\text{ rt)}[/tex]The interest that she would pay can be calculated using the formula:
[tex]\text{Interest = Amount - Principal}[/tex]The amount after 6 months is:
[tex]\begin{gathered} \text{Amount = 1100(1 + 007 }\times\frac{6}{12}) \\ =\text{ 1138.5} \end{gathered}[/tex]Hence, the interest:
[tex]\begin{gathered} \text{Interest = 1138.5 - 1100} \\ =\text{ 38.5} \end{gathered}[/tex]Answer: $38.5
Natural Logs Propertydo not include any spaces when trying to type in your answer if you have an exponent use ^
Given:
[tex]ln\mleft(e^{2x}\mright)+ln\mleft(e^x\mright)[/tex]To simplify:
Applying the log rule,
[tex]\log _c\mleft(a\mright)+\log _c\mleft(b\mright)=\log _c\mleft(ab\mright)[/tex]We get,
[tex]\begin{gathered} ln(e^{2x})+ln(e^x)=\ln (e^{2x}\cdot e^x) \\ =\ln (e^{3x}) \\ =3x(\ln e) \\ =3x(1) \\ =3x \end{gathered}[/tex]Hence, the answer is 3x.
у = -3х5х + y = 14i need help finding the matrix of this
3x + y = 0
5x + y = 14
[tex]\Delta\text{ = }\begin{bmatrix}{3} & 1{} & \\ {5} & 1{} & {} \\ {} & {} & {}\end{bmatrix}\text{ = (3 x 1) - (5 x 1) = 3 - 5 = -2}[/tex][tex]undefined[/tex]
Find all critical points of the function f(x) = x^3 + 5x^2 - 7x - 3.The critical point(s) is(are) =
We are given:
[tex]f(x)=x^3+5x^2-7x-3[/tex]Now, we know that in order to determine the critical points we derivate and the derivative is then equal to 0, that is:
[tex]f^{\prime}(x)=3x^2-10x-7=0[/tex]Now, we solve for x, that is:
[tex]3x^2+10x-7=0\Rightarrow x=\frac{-(10)\pm\sqrt[]{(10)^2-4(3)(-7)}}{2(3)}[/tex][tex]\Rightarrow\begin{cases}x=-\frac{5+\sqrt[]{46}}{3}\Rightarrow x\approx-3.9 \\ \\ x=\frac{-5+\sqrt[]{46}}{3}\Rightarrow x\approx0.6\end{cases}[/tex]So, the critical points of the function are:
[tex]\begin{cases}x=-\frac{5+\sqrt[]{46}}{3} \\ \\ x=\frac{-5+\sqrt[]{46}}{3}\end{cases}[/tex]Now, we determine the y-components of the points, that is:
[tex]\begin{cases}f(-\frac{5+\sqrt[]{46}}{3})=(-\frac{5+\sqrt[]{46}}{3})^3+5(-\frac{5+\sqrt[]{46}}{3})^2-7(-\frac{5+\sqrt[]{46}}{3})-3\Rightarrow f(-\frac{5+\sqrt[]{46}}{3})=41.03608735 \\ \\ f(\frac{-5+\sqrt[]{46}}{3})=(\frac{-5+\sqrt[]{46}}{3})^3+5(\frac{-5+\sqrt[]{46}}{3})^2-7(\frac{-5+\sqrt[]{46}}{3})-3\Rightarrow f(\frac{-5+\sqrt[]{46}}{3})=-5.184235498\end{cases}[/tex]So, the two critical points are:
[tex](-\frac{5+\sqrt[]{46}}{3},41.03608735)[/tex]and:
[tex](\frac{-5+\sqrt[]{46}}{3},-5.184235498)[/tex]This can be seing as follows:
can (x^4y)^(2/3) be simplified yes or no
Answer:
yes
we are need multiple the exponents in (x^4y)^(2/3).
[tex]x \frac{8y}{3} [/tex]
so hope it help
Answer:
[tex]x^\frac{8}{3} y^\frac{2}{3}[/tex]
Step-by-step explanation:
I'm not sure if you mean
[tex](x^4y)^\frac{2}{3}[/tex]
or
[tex](x^{4y})^\frac{2}{3}[/tex]
but I'll go with the first one
[tex](x^4y)^\frac{2}{3}[/tex]
(distribute the 2/3) (if the y is by it self, it basically is [tex]y^1[/tex])
[tex]x^\frac{8}{3} y^\frac{2}{3}[/tex]
done
8 nickels to 15 dimes what's the lowest terms
we have the quotient
8/15
remember that
8=2^3
15=3*5
8/15------> its irreducible
we have that
1 nickel=0.5 dimes
so
8 nickels=4 dimes
the ratio is
4/154/15Looking to receive help on the following practice question thank you.
use the definition of sec and write it in terms of cos
[tex]r=4\cdot\frac{1}{\cos \theta}[/tex]multiply both sides by cos
[tex]r\cos \theta=4[/tex]then we know that r*cos is equal to x in the cartesian
[tex]x=4[/tex]HELP PLEASEEEEE!!!!!!
A rational number that is between -0.45 and -0.46 is -0.455.
What is the rational number?The values given are negative decimal numbers. A decimal is a method that is used to write non-integers. An example of a decimal is 0.48. A negative number is a number whose value is less than one.
A rational number is a number that can be expressed as a fraction of two integers
Examples of rational numbers are 2 , -0.455.
-0.455 can be expressed as an integer of -0.22750 and 0.22750.
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Marshawn has batting average of 0.727272... write his batting average as fraction in simplest form
Marshawn batting average as fraction in simplest form is 90909/125000.
Given a number into decimal form i.e., 0.727272...
Marshawn has batting average of 0.727272....
And, Write his batting average as fraction in simplest form.
Based on the given conditions,
Formulate:
0.727272..
Simplify in simplest form:
0.727272/1
= 7.27272/10
=72.7272/100
= 727.272/1000
= 7272.72/10000
=72727.2/100000
=727272/1000000
It is divided by 2, we get
= 363636/ 500,000
= 181,818/ 250,000
= 90909/125000
Hence, Marshawn batting average as fraction in simplest form is 90909/125000.
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A parallelogram has an 9 inch base. if the parallelogram has an area of 54 square inches, find the height of the parallelogram.
In order to find the height of the parallelogram, we can use the following formula for its area:
[tex]A=b\cdot h[/tex]Where A is the area, b is the base and h is the height of the parallelogram.
Using A = 54 and b = 9, we can solve the equation for h:
[tex]\begin{gathered} 54=9\cdot h \\ h=\frac{54}{9} \\ h=6 \end{gathered}[/tex]So the height of the parallelogram is 6 inches.
2) through: (-2,5), perp. to 1 = 7 1 1 LU perp m 1 2 b Sub y, m, and
Answer:
y = (-7/2)x - 2
Step-by-step explanation:
Equation of a line:
The equation of a line is given by:
y = mx + b
In which m is the slope and b is the intercept.
We want the equation of a line perpendicular to y = (2/7)x - 4.
This slope is 2/7.
When two lines are perpendicular, the multiplication of their slopes is -1.
We want to find m. So
(2/7)*m = -1
2m = -7
m = (-7/2)
So
y = (-7/2)x + b
Through the point (-2,5):
This means that when x = -2, y = 5. So
y = (-7/2)x + b
5 = (-7/2)*(-2) + b
7 + b = 5
b = 5 - 7
b = -2
So, the equation is:
y = (-7/2)x - 2
I need help Options for the first box: -3, 1/3, 3, -1/3 Options for the second box -303, 363, 183, -60
To find the common ratio of the sequence, divide each of the elements of the sequence by the element that precedes it:
[tex]\begin{gathered} \frac{-9}{3}=-3 \\ \frac{27}{-9}=-3 \\ \frac{-81}{27}=-3 \end{gathered}[/tex]Since the quotient is always -3, then the common ratio is equal to -3.
To find the fifth term of the sequence, multiply the fourth term, which is -81, times -3:
[tex]-81\times-3=243[/tex]Once that we know the first five terms of the sequence, add them to find their sum:
[tex]\begin{gathered} 3-9+27-81+243 \\ =-6+27-81+243 \\ =21-81+243 \\ =-60+243 \\ =183 \end{gathered}[/tex]Therefore:
The common ratio of the sequence is -3.
The sum of the first five terms of the sequence is 183.
What is the greatest common factor of 28y^2 and 49y^2?A. 196y^2B. 7y^2C. 21y^2D. 7y
the value is 7 and keep the y^2
so is
[tex]7y^2[/tex]the difference between 58% of a number and 39% of the same number is 247. what is 62% of that number
Answer
62% of the number = 806
Explanation
We are told that that the difference between 58% of a number and 39% of the same number is 247.
We are then asked to compute 62% of the number.
Let the number be x.
From the first statement,
58% of x = 0.58 × x = 0.58x
39% of x = 0.39 × x = 0.39x
The difference between them is 247
0.58x - 0.39x = 247
0.19x = 247
Divide both sides by 0.19
(0.19x/0.19) = (247/0.19)
x = 1300
So, we can now calculate 62% of the number
62% of x = 0.62 × x = 0.62 × 1300 = 806
Hope this Helps!!!
Please hurry!!!
Is there a relationship between the distance and the sum? Is there a relationship between the distance and the difference?
A 5-column table with 3 rows. Column 1 is labeled a with entries 1, 4, negative 6. Column 2 is labeled b with entries 2, negative 1, negative 3. Column 3 is labeled a + b with entries 3, 3, negative 9. Column 4 is labeled a minus b with entries negative 1, 5, negative 3. Column 5 is labeled Distance with entries 1 unit, 5 units, 3 units.
Which describes the relationship between the distance and the difference?
The distance is always the opposite of the difference.
The distance is exactly the difference.
The distance is the absolute value of the difference.
The distance is not related to difference.
The third option that is the distance is the absolute value of the difference describes the relationship between distance and difference.
We know that the distance between two points is the difference of those two values.
But as the distance between two points can never be negative, we will write the absolute value of the difference as the distance between the two points.
Here we can see that,
a - b = -1 when distance = 1
a - b = 5 when distance = 5
a - b = 3 when distance = 3
Hence, the relationship between difference and distance is described by the third option.
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need help with this problem answer in a quick and clear response
Answer:
A system of inequalities with parallel boundaries doesn't have a solution when the regions for each inequality don't intersect. This region depends on the sign of inequality, so the signs of inequality determine if the system has solutions.
I need to send a picture in order to answers the question because it has a graph.
The dotted plot representing how much a customer spends in a store from the attached diagram is Option D.
Step 1: Write out the frequency distribution of the population in tabular form
x | f
------------------------------------------
5 | 17
------------------------------------------
| 17
------------------------------------------
when the occurrence of one event precludes the occurrence of the other the events are said to be what
Answer:
Mutually Exclusive.
Explanation:
When the occurrence of one event prevents or affects the occurrence of the other, the events are said to be Mutually Exclusive.
Consider the following relation. y= 2x-4
Find four points contained in the inverse. Express your values as an integer or simplified fraction.
ASAP PLEASE¡
Four points that are contained in the inverse function include the following:
Point = (0, 4).Point = (1, 4.5).Point = (2, 5).Point = (4, 6).What is an inverse function?An inverse function refers to a type of function that is obtained by reversing a mathematical operation in a given function (f(x)).
In order to determine the inverse of the given function, we would interchange both the input value (x) and output value (y) as follows:
y = 2x - 4
x = 2y - 4
Subtracting 4 from both sides, we have:
x + 4 = 2y - 4 + 4
2y = x + 4
Dividing both sides by 2, we have:
y = (x + 4)/2
y = x/2 + 4
When x = 0, we have:
y = x/2 + 4
y = 0/2 + 4
y = 4
Point = (0, 4).
When x = 1, we have:
y = x/2 + 4
y = 1/2 + 4
y = 4.5
Point = (1, 4.5).
When x = 2, we have:
y = x/2 + 4
y = 2/2 + 4
y = 5
Point = (2, 5).
When x = 4, we have:
y = 4/2 + 4
y = 0/2 + 4
y = 6
Point = (4, 6).
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