Answers
The area = area of the big rectangel - sum of the areas of the two circles
the diameter of each of the circles is 10.5cm
Hence, each circle has a radius of 10.5cm / 2 = 5.25cm
The length of the rectangle = the sum of the diameters of the circles
Therefore
The length of the rectangle = 10.5cm + 10.5cm = 21cm
The width of the rectangle = 10.5cm
Hence,
[tex]\begin{gathered} \text{area of shaded portion = 21}\times10.5\text{ - (}\pi\times5.25^2+\pi\times5.25^2) \\ =220.5-(55.125\pi)\approx47.32 \end{gathered}[/tex]Hence the area of the shaded portion is 47.32 square centimeters
Related Questions
how do u knwo which way to face the inequality sign in the answer of these questions like 1>x<3 how do u know which way to face them. i put some examples os u cna use them to explain
Answers
Using the graph identify the intervals:
a) Function being less than or equal to 0: In which x interval is the graph under the x-axis (the functions are less than 0 when they are under x-axis)
As the ineqaulity sing is less than or equal to 0, the interval includes those x-values for which the function is 0:
Solution: Interval from x=1 to x=3
[tex]\begin{gathered} x^2-4x+3\leq0 \\ 1\leq x\leq3 \\ \lbrack1,3\rbrack \end{gathered}[/tex]b) Function being greater than or equal to 0: In which x interval is the graph over the x-axis.
As the ineqaulity sing is greater than or equal to 0, the interval includes those x-values for which the function is 0:
Solution: Interval from - infinite to 1 and from 3 to infinite
[tex]\begin{gathered} x^2-4x+3\ge0 \\ 1\ge x\ge3 \\ (-\infty,1\rbrack\cup\lbrack3,\infty) \end{gathered}[/tex]c) Function being greater than 0: In which x interval is the graph over the x-axis.
As the ineqaulity sing is greater than to 0, the interval does not include those x-values for which the function is 0.
[tex]\begin{gathered} x^2-4x+3>0 \\ 1>x>3 \\ (-\infty,1)\cup(3,\infty) \end{gathered}[/tex]d) Function being less than 0: In which x interval is the graph under the x-axis.
As the ineqaulity sing is less than 0, the interval does not include those x-values for which the function is 0:
[tex]\begin{gathered} x^2-4x+3<0 \\ 1The lengths of the diagonals of a rectangle are representedby 2x + 3 and 4x - 11. Find the value of x.
Answers
The problem says that there are formulas for the diagonals of a rectangle. they are both givan in terms of x
Now, recall that the diagonals of a rectangle should be equal to each other, therefore those two expressions must equal ech other
2 x + 3 = 4 x - 11
Now let's solve for x:
move all terms with "x" to one side of the equation, and all "numerical" terms to the other side:
start by subtracting 2x from both sides:
3 = 4 x - 2 x - 11
3 = 2 x - 11
Now add 11 to both sides:
11 + 3 = 2 x
14 = 2 x
then x is 7
+10B-10-8-644810Bc8--10and aWe can show that ABC is congruent to AA'BC by a translation ofunits)across the-axis.
Answers
ANSWER
ABC is congruent to A'B'C' by a translation of 2 units and a reflection across the x-axis
EXPLANATION
We want to identify the transformations that were carried out on ABC to obtain A'B'C'.
First, we notice that A'B'C' is not aligned with ABC because the vertex of B' is 2 units behind the vertex of B.
So, we can say that there was a translation of 2 units to the left or -2 units..
Also, we notice that the vertices of ABC were flipped over the x-axis to obtain A'B'C'.
Therefore, we can conclude that there was a reflection across the x axis.
Hence, ABC is congruent to A'B'C' by a translation of 2 units and a reflection across the x-axis.
A hot air balloon is flying above Groveburg. To the left side of the balloon, the balloonist measure the angle of depressionto the Groveburg soccer fields to be 20° 15'. To the right side of the balloon, the balloonist measures the angle ofdepression to the high school football field to be 62° 30'. The distance between the two athletic complexes is 4 miles.What is the distance from the balloon to the football field?a.b.>3.6 miC.~6.2 mi>2.2midy1.4 miPlease select the best answer from the choices providedOAOBOCOD
Answers
The distance from the balloon to the football field will be 1.4 miles.
Angle of depression to the Grove burg soccer fields = 20° 15'.
Use 1' = 1 / 60° :
15' = 1 / 4 ° = 0.25 °
20° 15' = 20.25°
Angle of depression to the high school football field = 62° 30'.
30' = 0.5°
62° 30' = 62.5°
the distance from the balloon to the football field will be:
Let the distance be a
a / sin a = c / sin c
a / sin (20.25) = 4 / sin (97.5)
a = 4 sin (20.25) / sin (97.5)
a = 1.4 miles.
Therefore, we get that, the distance from the balloon to the football field will be 1.4 miles.
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l A golf ball is hit in the air. The table shown describes y, the height of the ball, in feet, given the time elapsed, x, in seconds, since the time the ball was hit.Based on the information in the table, which statements are true? Select each correct statement.
Answers
Given:
y is the height of the ball in feet
x is the time in seconds
In the given table you can identify the next maximum:
x=3
y=30
The ball has height 0 when it is in the earth so it is hit at second 0 and will be back in the earth at second 6
Then, from the given statements the next are true:
The maximum height of the ball was 30 feetThe ball was in the air for only 6 secondsIf AABC = ADEC,ZB = 44º and ZE = 4xx= [?]
Answers
Solution
Given that Triangle, ABC is congruent to Triangle DEC
=> ∠A = ∠D; ∠B = ∠E; ∠C = ∠C
Given that ∠B = 44, ∠E = 4x
=> 44 = 4x
=>x = 44/4 = 11
Hence, x = 11
sec40+ sec20 tan2 0 - 2 tan4 0 =3 sec² 0 -2Sect0-210
Answers
Given:
[tex]sec^4\theta+sec^2\theta tan^2\theta-2tan^4\theta=3sec^2\theta-2[/tex]Required:
We need to prove the given equation.
Explanation:
Consider the left-hand side of the equation.
[tex]Add\text{ and subtract }3tan^4\theta.[/tex][tex]sec^4\theta+sec^2\theta tan^2\theta-2tan^4\theta=sec^4\theta+sec^2\theta tan^2\theta-2tan^4\theta+3tan^4\theta-3tan^4\theta[/tex][tex]=sec^4\theta+sec^2\theta tan^2\theta+tan^4\theta-3tan^4\theta[/tex][tex]Add\text{ and subtract -2}sec^2\theta tan^2\theta.[/tex][tex]=sec^4\theta+sec^2\theta tan^2\theta+tan^4\theta-3tan^4\theta-2sec^2\theta tan^2\theta+2sec^2\theta tan^2\theta[/tex][tex]=sec^4\theta-2sec^2\theta tan^2\theta+tan^4\theta-3tan^4\theta+sec^2\theta tan^2\theta+2sec^2\theta tan^2\theta[/tex][tex]=sec^4\theta-2sec^2\theta tan^2\theta+tan^4\theta-3tan^4\theta+3sec^2\theta tan^2\theta[/tex][tex]Use\text{ }sec^4\theta-2sec^2\theta tan^2\theta+tan^4\theta=(sec^2\theta-tan^2\theta)^2[/tex][tex]=(sec^2\theta-tan^2\theta)^2-3tan^4\theta+3sec^2\theta tan^2\theta[/tex][tex]=(sec^2\theta-tan^2\theta)^2+3tan^2\theta(sec^2\theta-tan^2\theta)[/tex][tex]Use\text{ }sec^2\theta-tan^2\theta=1.[/tex][tex]=1^2+3tan^2\theta(1)[/tex][tex]=1+3tan^2\theta[/tex][tex]Use\text{ }tan^2\theta=sec^2\theta-1.[/tex][tex]=1+3(sec^2\theta-1)[/tex][tex]=1+3sec^2\theta-3[/tex][tex]=3sec^2\theta-2[/tex]We get the right-hand side of the equation.
Final answer:
[tex]sec^4\theta+sec^2\theta tan^2\theta-2tan^4\theta=3sec^2\theta-2[/tex]Draw the image of the figure under thegiven transformation.6.reflection across the x-axis7. (X,y) - (x - 4, y + 1)8. reflection across the y-axis
Answers
6.
While transformation with the reflection across the x-axis, the absicssa (x-coordinate) remains the same but ordinate (y-coordinate) changes its sign.
The coordinate of point A is (3,0), coordinate of point B is (1,4) and the coordinate of point C is (5,3).
After transformation the, coordinate with the image can be shown as,
Thus, the coordinates of the image after transformation is A'(3,0), B'(1,-4) and C'(5,-3).
Write the equation of the line that is perpendicular to the line given and through the given point. Do not use spaces in your equation. y=-2X+1 (0,5) *
Answers
Answer:
y = 0.5x + 5
Explanation:
The equation of a line can be calculated as:
[tex]y=m(x-x_1)+y_1[/tex]Where m is the slope and (x1, y1) is a point in the line.
To find the slope of our line, we need to identify the slope of the given line.
Since the equation of the given line is y = -2x + 1, the slope of this line is -2, because it is the number beside the x.
Then, two lines are perpendicular if the product of their slopes is equal to -1. So, we can write the following equation:
[tex]-2\cdot m=-1[/tex]Therefore, the slope m of our line will be:
[tex]m=\frac{-1}{-2}=0.5[/tex]Now, we can replace the value f m by 0.5 and the point (x1, y1) by (0, 5) and we get that the equation of the line is:
[tex]\begin{gathered} y=0.5(x-0)+5 \\ y=0.5(x)+5 \\ y=0.5x+5 \end{gathered}[/tex]Therefore, the answer is y = 0.5x + 5
Consider functions f and g.1 + 12f(1) = 12 + 4. – 12for * # 2 and 7 -64.2 – 16. + 1641 +48for a # -12 Which expression is equal to f(x) · g(t)?OA.41 - 81 + 61OB.SIKIAOC.21 + 6I + 2D.6
Answers
Given the following functions below,
[tex]\begin{gathered} f(x)=\frac{x+12}{x^2+4x-12}\text{ and} \\ g(x)=\frac{4x^2-16x+16}{4x+48} \end{gathered}[/tex]Factorising the denominators of both functions,
Factorising the denominator of f(x),
[tex]\begin{gathered} f(x)=\frac{x+12}{x^2+4x-12}=\frac{x+12}{x^2+6x-2x-12}=\frac{x+12}{x(x+6)-2(x+6)}=\frac{x+12}{(x-2)(x+6)} \\ f(x)=\frac{x+12}{(x-2)(x+6)} \end{gathered}[/tex]Factorising the denominator of g(x),
[tex]\begin{gathered} g(x)=\frac{4x^2-16x+16}{4x+48}=\frac{4(x^2-4x+4)}{4(x+12)} \\ \text{Cancel out 4 from both numerator and denominator} \\ g(x)=\frac{x^2-4x+4}{x+12}=\frac{x^2-2x-2x+4}{x+12}=\frac{x(x-2)-2(x-2)}{x+12}=\frac{(x-2)^2}{x+12} \\ g(x)=\frac{(x-2)^2}{x+12} \end{gathered}[/tex]Multiplying both functions,
[tex]undefined[/tex]Write the equation in slope-intercept form through the point (2, -1) and is perpendicular to the line y = -5x + 1 and graph.
Answers
First, we are going to calculate the perpendicular slope. The condition for perpendicular lines is the following:
[tex]m1m2=-1[/tex]First, m1 = -5
[tex]m2=\frac{-1}{m1}=\frac{-1}{-5}\rightarrow m2=\frac{1}{5}[/tex]Now, for b
[tex]b=y-m2x[/tex]For the point (2,-1)
[tex]b=-1-\frac{1}{5}\cdot(2)[/tex][tex]b=-\frac{5}{5}-\frac{2}{5}=\frac{-7}{5}[/tex][tex]y=\frac{1}{5}x-\frac{7}{5}[/tex]A. Step 1B. Step 2C. Priya did not make a mistake
Answers
We will have the following:
[tex]\frac{f}{0.25}=16\Rightarrow f=16\cdot0.25[/tex][tex]\Rightarrow f=4[/tex]From this we can see that there was no mistaky on Priya's side. [Option 3]
A box contains different colored paper clips. The probability of drawing two red paper clips from the box without replacement is 1/7, and the probability of drawing one red paper clip is 2/5.What is the probability of drawing a second red paper clip, given that the first paper clip is red?1/65/142/32/35
Answers
SOLUTION
The probability of two red paper clips without replacement means
The probability of drawing the first and the probability of drawing the second one. This is represented as
[tex]P(R_{1st}\cap R_{2nd})[/tex]And this was given as
[tex]\frac{1}{7}[/tex]So
[tex]P(R_{1st}\cap R_{2nd})=\frac{1}{7}[/tex]Probalilty of drawing one red paper clip is
[tex]P(R_{1st})=\frac{2}{5}[/tex]Now the probability of drawing a second red paper clip, given that the first paper clip is red becomes
[tex]\begin{gathered} P(R_{1st}/R_{2nd})=\frac{P(R_{1st}\cap R_{2nd})}{P(R_{1st})} \\ \\ P(R_{1st}/R_{2nd})=\frac{\frac{1}{7}}{\frac{2}{5}} \\ \\ =\frac{5}{14} \end{gathered}[/tex]Hi, can you help me answer this question please, thank you!
Answers
Given that
[tex]\begin{gathered} \mu_1=sample\text{ of soda in the coke can} \\ \mu_2=sample\text{ of soda in the pepsi can} \end{gathered}[/tex]Therefore, in the first statement, we are to test how accurate the companies package these cans.
Mathematically it can be expressed as,
[tex]H_0\colon\mu_1\leq\mu_2[/tex]In the second statement, we wish to test the claim that the mean of the amount of liquid in coke cans is greater than the amount of liquid in pepsi cans. This can be expressed mathematically as,
[tex]H_a\colon\mu_1>\mu_2[/tex]Hence, the correct option is Option 1.
Determine the probability of being dealt 4 Aecs of cards, from a deck of 52 playing cards, with a replacement.
Answers
Given:
4 Aces of cards from a deck of 5 playing cards.
[tex]\begin{gathered} \text{Probability of drawing 4 Aces }=\frac{4}{52}\times\frac{4}{52}\times\frac{4}{52}\times\frac{4}{52}\times4! \\ \text{Probability of drawing 4 Aces }=\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}\times24 \\ \text{Probability of drawing 4 Aces }=\frac{24}{28561} \end{gathered}[/tex]What is this expression in simplest form?
+2
4x² + 5x + 1
Ο Α.
О в.
O C.
O D.
4x + 1
²-4
(x + 1)(x − 2)
-
I
(z = 2)
1
4x + 1
(x + 1)(x-2)
ww
4x+1
#12
Answers
Answer:
[tex] \frac{x + 2}{4 {x}^{2} + 5x + 1 } . \frac{4x + 1}{ {x}^{2} + 4} \\ \frac{x + 2}{4 {x}^{2} + (4 + 1)x + 1 } . \frac{4x + 1}{ {(x + 2)}^{2} } \\ \frac{1}{4 {x}^{2} + 4x + x + 1}. \frac{4x + 1}{x + 2} \\ \frac{1}{x(4x + 1) + 1(4x + 1)} . \frac{4x + 1}{x + 2} \\ \frac{1}{(4x + 1)(x + 1)} . \frac{4x + 1}{x + 2} \\ \frac{1}{(x + 1)}. \frac{1}{(x + 2)} \\ \frac{1}{(x + 1)(x + 2)} [/tex]
A. is the answer!!
The value of 0.36 when converted to a fraction in the simplest form is 9/25.
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
here, we have,
to calculate fractions in simplest form:
Your information is incomplete. Therefore, an overview will be given. It should be noted that a fraction is in its simplest form when the numerator and denominator are prime.
From example, let's convert 0.36 to a fraction on its simplest form. This will be:
0.36 = 36/100 = 9/25
In conclusion, 0.36 is 9/25 in the simplest form.
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How to do 2 step equations Can you solve 2x + 5=21?
Answers
Given
The equation,
[tex]2x+5=21[/tex]To find the value of x or to solve for x.
Explanation:
It is given that,
The equation is,
[tex]2x+5=21[/tex]That implies,
[tex]\begin{gathered} 2x+5=21 \\ 2x=21-5 \\ 2x=16 \\ x=\frac{16}{2} \\ x=8 \end{gathered}[/tex]Hence, the value of x is 8.
a cellular phone company charges a base rate of $15.00 per month and $0.05 per minute,m, which equation could be used to find the total monthly charge in dollars,c?
Answers
Suppose you use "m" minutes in a month and each minute is $0.05, so your minute bill would be:
0.05 * m
Per month, there is a fixed rate of $15 , no matter how many minutes you use.
So, that's a fixed cost.
Total monthly charge would be:
15 + 0.05m
The cost, c, is:
[tex]c=0.05m+15[/tex]Correct Answer Choice is Option B
The product of two whole numbers is 592 and their sum is 53. What are the two numbers?
Answers
To solve this problem, we have to build two equations with the given information. Using x and y to represent the two numbers:
• Equation 1
[tex]x\times y=592[/tex]• Equation 2
[tex]x+y=53[/tex]Now that we have to equations, we have to isolate one variable from one equation and replace it in the other.
[tex]x=53-y[/tex]Then, we will replace this value of x in Equation 1:
[tex](53-y)\cdot y=592[/tex]Solving for y we get:
[tex]53y-y^2=592[/tex][tex]-y^2+53y-592=0[/tex]As we got this expression, we will have to use the General Quadratic Formula. With the help of a calculator, we get both values:
[tex]y_1=16[/tex][tex]y_2=37[/tex]Finally, we have to replace these values in Equation 1 to evaluate which meets the condition:
[tex]x_1=\frac{592}{y_1}[/tex][tex]x_1=\frac{592}{16}=37[/tex][tex]x_2=\frac{592}{y_2}[/tex][tex]x_2=\frac{592}{37_{}}=16[/tex]We have to evaluate the values in each equation:
[tex]\begin{gathered} 37+16=53 \\ 53=53 \end{gathered}[/tex][tex]37\cdot16=592[/tex]The first numbers meet the condition.
Answer: 37 and 16
Write the expression and simplifyThe difference of -10 and the product of p and q
Answers
We start with a subtraction, where we want to subtract the second term from - 10. The second term consists in a multiplication between p and q. Writing this as a mathematical expression we have
[tex]-10-pq[/tex]This expression is already on simplest form.
Justin earned $600 last week fixing computers.Is it possible to determine how many hours Justin worked?explain
Answers
Since Justin earned $600 last week
If we want to find the number of hours that he worked, we must have how much he earned per hour
But we do not have how much did he earn per hour, so
It is impossible to find how many hours did he work from the given information
The answer is
No, it is impossible to find that
Triangle A'B'C' is apparently - у А A' B C С B' O A clockwise 90 degree rotation of Triangle ABC O A reflection across the y-axis of Triangle ABC O A translation of Triangle ABC right 7 units O A clockwise 270 degree rotation of Triangle ABC
Answers
Since all coordinates of the transformated triangle are changed like this:
[tex](x,y)\rightarrow(y,-x)[/tex]Triangle A'B'C' is a clockwise 270 degree rotation of triangle ABC
A counterclockwise rotation of 90º is the same that a clockwise rotation of 270º
Determine the height of the ball after 4 seconds *Height of Ball over Time160144128112Height (in feet)96NO643216O1 2 3 4 5 6Time (in seconds)
Answers
80 ft
1) In the graph, we can find out the height after 4 seconds simply locating the point when the x-axis at t=4
2) Hence, after 4 seconds the height of the ball is:
3) Hence, the answer is 80 ft (the blue dot) (4,80)
What is the surface area of a pyramid if its one triangular face has an area of 20 sq. cm and its square base has a side of 5cm?A. 100 sq.cmB. 105 sq.cmC. 110 sq. cmD. 115 sq.cm
Answers
To solve this problem, we will use the following formula for the surface area of a square pyramid:
[tex]SA=BA+4A_t,[/tex]where BA= base area, and A_t is the area of one of the lateral triangles.
Now, we are given that:
[tex]A_t=20cm^2.[/tex]Recall that the area of a square is given by the following formula:
[tex]A_s=side^2.[/tex]We are given that the side of the base is 5 cm long, therefore, the base area is:
[tex]A_s=(5cm)^2=25cm^2.[/tex]Finally, we get that:
[tex]SA=25cm^2+4(20cm^2)=105cm^2.[/tex]Answer:
[tex]105cm^2.[/tex]Given that: 100 = 2^2 * 5^2, how is 400 written as a product of its prime factors?
Answers
Answer:
400 written as a product of it's prime factors is 2^4 * 5²
Step-by-step explanation:
We have to factore the number, dividing by prime factors(2, 3, 5, 7, ...)
400|2
200|2
100
We already have the factorization of 100. So
400 = 2²*100 = 2²*2²*5² = 2^4 * 5²
400 written as a product of it's prime factors is 2^4 * 5²
2^2*10^2=400
2^2=4
10^10=100
4*100=400
The surface area of a rectangular prism is 60. Which of the following are possible dimensions of the rectangular prism? 1 Pt
Answers
The surface area of a rectangular prism with sides a, b and c is given by the formula:
[tex]S=2(ab+ac+bc)[/tex]Use that formula to find the surface area that a prism with the given dimensions on each option would have.
A. 6, 2, 1 1/2
[tex]\begin{gathered} S=2(6\cdot2+6\cdot1\frac{1}{2}+2\cdot1\frac{1}{2}) \\ =2(12+9+3) \\ =2(24) \\ =48 \end{gathered}[/tex]B. 5, 4, 1 1/4
[tex]\begin{gathered} S=2(5\cdot4+5\cdot1\frac{1}{4}+4\cdot1\frac{1}{4}) \\ =2(20+\frac{25}{4}+5) \\ =2(\frac{125}{4}) \\ =\frac{125}{2} \\ =62.5 \end{gathered}[/tex]C. 3, 4, 1 1/2
[tex]\begin{gathered} S=2(3\cdot4+3\cdot1\frac{1}{2}+4\cdot1\frac{1}{2}) \\ =2(12+3\frac{3}{2}+6) \\ =2(21\frac{3}{2}) \\ =45 \end{gathered}[/tex]D. 6, 3, 1 1/3
[tex]\begin{gathered} S=2(6\cdot3+6\cdot1\frac{1}{3}+3\cdot1\frac{1}{3}) \\ =2(18+8+4) \\ =2(30) \\ =60 \end{gathered}[/tex]Therefore, the only possible dimensions of a rectangular prism with surface area 60 listed on the options, are 6, 3 and 3 1/3. The answer is:
[tex]\text{Option D}[/tex]katie has 5.455 apples and sadie has 10.31 how many apples do they have in all
Answers
Katie has 5.455
Sadie has 10.31
To find how many apples they have in all add the two numbers
They have = 5.455 + 10.31
They have = 5.455 + 10.310
0 + 5 = 5
1+ 5 = 6
3 + 4 = 7
10 + 5 = 15
They have = 15.765 apples in all
Solve the system of equations.y = x2 - 2y = -2x + 1A. (-3,7) and (-1,3)B. (-3,7) and (1, -1)C. (1.-1) and (3,-5)D. (-1,3) and (3, -5)
Answers
Answer
Option B is correct.
the solutions to the system of equations include
(-3, 7) and (1, -1)
Step-by-step Explanation
The question is to solve the system of equations
y = x² - 2 ..... equation 1
y = -2x + 1 ..... equation 2
To solve this, we can just equate the expression given for y in equation 1 to the expression given for y in equation 2.
y = x² - 2
y = -2x + 1
Since
y = y
x² - 2 = -2x + 1
x² + 2x - 2 - 1 = 0
x² + 2x - 3 = 0
This gives a quadratic equation which we will now solve
x² + 2x - 3 = 0
x² + 3x - x - 3 = 0
x (x + 3) - 1 (x + 3) = 0
(x - 1) (x + 3) = 0
So,
x - 1 = 0 or x + 3 = 0
x = 1 or x = -3
If x = 1,
y = x² - 2
= 1² - 2
= 1 - 2
= -1
x = 1, y = -1
If x = -3
y = x² - 2
= (-3)² - 2
= 9 - 2
= 7
x = -3, y = 7
So, the solutions to the system of equations include
x = -3, y = 7, that is, (-3, 7)
And
x = 1, y = -1, that is, (1, -1)
Hope this Helps!!!
in a survey of 1300 people who owned a certain type of car 585 said they would buy the type of car again what percent of people surveyed were satisfied with the car
Answers
In order to find the percentage of people that were satisfied with the car, we just need to divide this amount of people by the total amount of people surveyed.
So we have:
[tex]\frac{585}{1300}=0.45=45\text{\%}[/tex]So 45% of the surveyed people were satisfied with the car.
A phone company charges for service according to the formula: C(n) = 19 + 0.08n , where n is the number of minutes talked , and C(n) is the monthly charge, in dollars .The rate of change in this equation is:The initial value in this equation is:
Answers
In a linear equation, the coefficient of the variable is the rate of change and the constant term is the initial value.
For example, a linear function with rate of change m and initial value b is:
[tex]f(x)=mx+b[/tex]In the given formula, the variable is n, its coefficient is 0.08 and the constant term is 19.
Since n is measured in minutes and C is measured in dollars (as well as the initial value), then, the coefficient 0.08 must have the units necessary for the minutes to cancel out, leaving dollars as the unit of 0.08n. Then, the units of the rate of change must be dollars per minute.
Since the constant term is 19, then the initial value is 19.
Therefore, the answers are:
The rate of change in the equation is 0.08 dollars per minute.
The initial value in the equation is 19 dollars.