Assuming that boy and girl babies are equally likely, what would be Kathy's probability of having at most one daughter if she
were to have four children altogether? (You may want to use a tree diagram to construct the sample space.)
The probability is
(Type an integer or a simplified fraction.)
Answers
Answer: 0.3125.
Step-by-step explanation:
The chance of having a boy is 0.5, the chance of having a girl is also 0.5.Outcome 1: all boys
boy boy boy boy
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
Outcome 2: first child is a girl, all others are boys
girl boy boy boy
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
Outcome 3: second child is a girl, all others are boys
boy girl boy boy
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
Outcome 4: third child is a girl, all others are boys
boy boy girl boy
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
Outcome 5: fourth child is a girl, all others are boys
boy boy boy girl
0.5 * 0.5 * 0.5 * 0.5 = 0.0625
Therefore,
0.0625 + 0.0625 + 0.0625 + 0.0625 + 0.0625 = 0.0625 * 5 = 0.3125
Related Questions
What is the sec 132 degrees 15 minutes in degrees
Answers
The sec 132 degrees 15 minutes in degrees is approximately -1.638 degrees.
What is the sec function?The secant function, denoted as sec(x), is a trigonometric function that is defined as the reciprocal of the cosine function, cos(x).
In other words,
sec(x) = 1 / cos(x)
The secant function is defined for all values of x except for those where the cosine function is equal to zero, which corresponds to the values x = (2n+1)π/2 where n is an integer. At these points, the secant function is undefined.
According to the given informationTo convert sec(132 degrees 15 minutes) to degrees, we first need to convert the angle to decimal degrees.
We know that 1 degree is equal to 60 minutes, so 15 minutes is equal to 15/60 = 0.25 degrees.
Therefore, the angle 132 degrees 15 minutes is equal to 132 + 0.25 = 132.25 degrees.
Now we can find the secant of this angle:
sec(132.25 degrees) = 1/cos(132.25 degrees) ≈ -1.638
So the answer is approximately -1.638 degrees.
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(c) Problem 17:
How far will the baseball have dropped after
4.5 seconds?
(first taught in
lesson 90)
Afton
Answers
After 4.5 seconds, the baseball will have dropped approximately 99.35 meters.
To find out how far the baseball will have dropped after 4.5 seconds, we need to use the free fall formula.
The terms involved in this calculation are:
Time (t): 4.5 seconds.
Acceleration due to gravity (g): 9.81 m/s² (approximated)
Distance dropped (d)
The free fall formula is:
\(d = (1/2) \times g \times t^{2}\)
Now, we will plug in the given values and solve for d:
Substitute the values
\(d = (1/2) \times 9.81 \times (4.5)^{2}\)
Calculate the square of time
\(d = (1/2) \times 9.81 \times 20.25\)
Multiply the values
d = 99.3525.
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A media research company increased the size of their random samples from 3 comma 500to 5 comma 000.By how much, to the nearest tenth of a percent, did this improve their margin of error?
Answers
Step-by-step explanation:
If a media research company increased the size of their random samples from 3,500 to 5,000, to get the percentage margin error, we will follow the steps;
Initial sample size = 3500
Final sample size = 5000
margin error = Final sample size - initial sample size
Margin error = 5000-3500
Margin error = 1500
%margin error = Margin error/Initial sample size * 100%
%margin error = 1500/3500 * 100%
%margin error = 3/7 * 100%
%margin error = 300/7
%margin error = 42.86%
This means that they improved their margin by 42.9% (to the nearest tenth)
Select all of the statements that are true about f(x) =
1
А.
f(x) is an odd function.
B.
f(x) = f (2)
C
f(x) decreases from (-00, 0) U (0,0).
D.
f(x) is a rational function.
Answers
Answer:
3-4
Step-by-step explanation:
thats the answer because i need more points
I need to know the percentage of drivers who are at least 45. Using the table in the picture.
Answers
The percentage of drivers who are at least 45 is 62%
How to determine the percentage of drivers who are at least 45.From the question, we have the following parameters that can be used in our computation:
The table of values
From the table, we have
Age 45 = 62 percentile
When represented properly
So, we have
Age 45 = 62%
This means that the percentage of drivers who are at least 45 is 62%
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1. If <1 is 120 degrees , what is the measure of <2?
Answers
Answer:
240
Step-by-step explanation:
2 is 1 + 1 so 120 + 120 must be the equivalent of 2.
Jeremiah jumped forward 4 times. Each time his jump measured 24.4 cm. What is the total length of his four jumps? Write your answer using numbers only.
Answers
Answer:
97.6
Step-by-step explanation:
you multiply 24.4 and 4 to get your answer
quadratic regression for (1,-8) (2,-4) (3,6)
Answers
The quadratic regressiοn equatiοn fοr the given data pοints is y = 5x² - 20x + 7
What is quadratic equatiοn?
A secοnd-degree equatiοn οf the fοrm ax² + bx + c = 0 is knοwn as a quadratic equatiοn in mathematics. Here, x is the variable, c is the cοnstant term, and a and b are the cοefficients.
Tο find the quadratic regressiοn equatiοn fοr the given data pοints, we need tο fit a quadratic equatiοn οf the fοrm y = ax² + bx + c tο the data.
We can start by using the three given pοints tο set up a system οf three equatiοns:
\((1,-8): a(1)^2 + b(1) + c = -8\\\\(2,-4): a(2)^2 + b(2) + c = -4\\\\(3,6): a(3)^2 + b(3) + c = 6\)
SimpIifying each equatiοn, we get:
a + b + c = -8 (equatiοn 1)
4a + 2b + c = -4 (equatiοn 2)
9a + 3b + c = 6 (equatiοn 3)
AIternativeIy, we can use technοIοgy such as a caIcuIatοr οr spreadsheet tο sοIve the system.
SοIving the system using technοIοgy, we get:
a = 5
b = -20
c = 7
Therefοre, the quadratic regressiοn equatiοn fοr the given data pοints is:
y = 5x² - 20x + 7
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if a is a set of real numbers which is bounded above and b is a set of real numbers which is bounded below then there is at most one real number in both a and b?
Answers
If a is a set of real numbers that is bounded above and b is a set of real numbers that is bounded below, there is at most one real number that can exist in both sets.
A real number is any number that can be expressed as a decimal or fraction and exists on the number line.
If a set of real numbers, represented by a, is bounded above, it means that there exists a real number, represented by M, such that all the numbers in the set are less than or equal to M. Similarly, if a set of real numbers, represented by b, is bounded below, it means that there exists a real number, represented by m, such that all the numbers in the set are greater than or equal to m.
Now, let's consider a real number, represented by x, that exists in both sets a and b. If x exists in a, it must be less than or equal to M and if x exists in b, it must be greater than or equal to m. Hence, x must satisfy both conditions: M >= x >= m.
From these conditions, it can be deduced that M and m must be equal to x. In other words, there can only be one real number that is simultaneously the greatest value in a and the smallest value in b.
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what is (2) (-3) (-4)
Answers
Answer:
I believe it is 24
Step-by-step explanation:
(2) (-3) (-4)
(-6) (-4)
24
if 5x - 3 > 4 - x what is a possible value of x
Answers
Answer:
5x-3>4-x
5x+x>4+3
6x>7
6x/6>7/6
x>7/6.
Answer:
7/6 or 1 1/6
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
A student scores 80% on a 30 question test. Use a percent equation to write the ratio of the actual number of questions answered correctly to the actual total number of questions.
Answers
Answer:
80% of 30
= 30 × 0.8
= 24
So the student answered 24 out of 30 questions correctly.
Answer:
24
Step-by-step explanation:
80/100 × 30=24 answers he got right
24/30 questions are right
to check we can multiply 24/30 ×100 to get 80%
5
4
3-
Mark this and return
N
-5-4-3-2-1₁.
24
1+
GAW N
y
+2+
-3
-4
1 2 3 4 5 x
What is the range of the function on the graph?
O all the real numbers
O
all the real numbers greater than or equal to 0
all the real numbers greater than or equal to 2
O all the real numbers greater than or equal to -3
Save and Frit
Answers
The range of the function on the graph would be: D. all real numbers greater than or equal to 2
How to calculate the function rangeTo obtain the range, observe the y values whose result can be obtained by the function of x. To obtain this range, we examine the graph and note that the range begins from 2 on the y-axis and extends upwards.
So, if we wish to define our range, we will enter all real numbers that are equal to or greater than 2 as seen in the direction of the graph.
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HELP! Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the
rounded values to calculate the next value. Round your final answer to the nearest tenth.
Answers
Answer:
b
Step-by-step explanation:
In complete sentences explain how you would factor the numeric expression 34 + 12 + 20.
Answers
Answer:
We are asked to determine the correct factorization of the given trinomial which is 5x² - 5x -100. The solution to this problem is shown below:
5x² - 5x - 100 let the problem equal to zero such as:
5x² - 5x - 100 = 0 , factor out 5 from the given trinomial
5(x²-x-20) = 0
5 (x-5)(x+4) = 0
The correct factor is 5(x-5)(x+4).
Step-by-step explanation:
What is the value of 21 over 4 − 32 over 5?
Answers
In linear equation, -1.15 is the value of 21 over 4 − 32 over 5.
What in mathematics is a linear equation?
An algebraic equation B. y=mx+b (where m is the slope and b is the y-intercept) containing simple constants and first-order (linear) components, such as the following, is called a linear equation. The above is sometimes called a "linear equation in two variables" where x and y are variables.
An equation with only one variable is called a univariate linear equation. It contains the expression Ax + B = 0. where A and B are any two real numbers and x is an ambiguous variable with only one possible value.
(21/4) - (32/5)
= 21 * 5 - 32 * 4/ 20
= 105 - 128/20
= -1.15
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Jack has baseball practice every third day and swimming practice every second day. During the month of February, how many days will Jack have both practices? ** hint: MONTH of FEBRUARY
Answers
Answer:
Jack will have both practices for 4 days of the month.
Step-by-step explanation:
I used a calendar and marked each day he would have swimming practice in green and each day he would have baseball practice in magenta accordingly. The days that had both marks were the days he had both practices, which was 4 days in total.
enrique needs our help again. He has 310 dollars he can afford to put towards a new car each month. he wants to be done in 5 years.
a. if he were to be approved for loan at 8% apr compounded monthly, what would the size loan granted to him be? what is he were approved for 3% compounded monthly?
b. one of your values should be higher then the other. Explain why it makes sense that your higher loan value paired with the apr that produced it makes sense?
Answers
Using the monthly payment formula, it is found that:
a. The sizes of the loans are given as follows:
8% interest rate monthly: $15,274.3% interest rate monthly: $17,252.b. Enrique can take the higher loan as the lower interest rate means that the amount will accumulate less over time.
Monthly payment formulaThe monthly payment formula is given by the following equation:
\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)
The parameters of the equation are described as follows:
P is the initial amount.r is the interest rate.n is the number of payments.In the context of this problem, the values of these parameters are as follows:
A = 310. (monthly payment he can afford).n = 60, as 5 years x 12 months = 60 payments.r/12 = 0.08/12 = 0.0067. -> case 1.r/12 = 0.03/12 = 0.0025. -> case 2.For case 1, the principal is calculated as follows:
\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)
\(310 = P\frac{0.0067(1 + 0.0067)^{60}}{(1 + 0.0067)^{60} - 1}\)
0.02029554306P = 310
P = 310/0.02029554306
P = $15,274.
For case 2, the principal is calculated as follows:
\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)
\(310 = P\frac{0.0025(1 + 0.0025)^{60}}{(1 + 0.0025)^{60} - 1}\)
0.01796869066P = 310
P = 310/0.01796869066
P = $17,252.
With the lower interest rate, the amount will accumulate less over time, hence we can take a higher loan.
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I need this practice problem answered I will provide the answer options in another pic
Answers
The inverse of a matrix can be calculated as:
\(\begin{gathered} \text{When} \\ A=\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {} \\ {} & {} & \end{bmatrix} \\ \text{Then A\textasciicircum-1 is:} \\ A^{-1}=\frac{1}{ad-bc}\begin{bmatrix}{d} & -{b} & {} \\ {-c} & {a} & {} \\ {} & {} & \end{bmatrix} \end{gathered}\)Then, let's start by calculating the inverse of the given matrix:
\(\begin{gathered} \begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}^{-1}=\frac{1}{4\cdot3-1\cdot(-2)}\begin{bmatrix}{3} & -{1} & {} \\ {-(-2)} & {4} & {} \\ {} & {} & \end{bmatrix} \\ \begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}^{-1}=\frac{1}{14}\begin{bmatrix}{3} & -{1} & {} \\ {2} & {4} & {} \\ {} & {} & \end{bmatrix} \end{gathered}\)The problem says he multiplies the left side of the coefficient matrix by the inverse matrix, thus:
\(\begin{gathered} \begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}^{-1}\begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}\cdot\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{4} & {1} & {} \\ {-2} & {3} & {} \\ {} & {} & \end{bmatrix}^{-1}\begin{bmatrix}{2} & {} & {} \\ {-22} & {} & {} \\ {} & {} & {}\end{bmatrix} \\ \end{gathered}\)*These matrices will be the options to put on the first and second boxes.
Then:
\(\begin{gathered} \begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\frac{1}{14}\begin{bmatrix}{3} & -{1} & {} \\ {2} & {4} & {} \\ {} & {} & \end{bmatrix}\cdot\begin{bmatrix}{2} & {} & {} \\ {-22} & {} & {} \\ {} & {} & {}\end{bmatrix}\text{ This is for the third box} \\ \begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\frac{1}{14}\begin{bmatrix}{3\times2+(-1)\times(-22)} & & {} \\ {2\times2+4\times(-22)} & & {} \\ {} & {} & \end{bmatrix}=\frac{1}{14}\begin{bmatrix}{28} & & {} \\ {-84} & & {} \\ {} & {} & \end{bmatrix}\text{ This is the 4th box} \\ \begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{28/14} & & {} \\ {-84/14} & & {} \\ {} & {} & \end{bmatrix}=\begin{bmatrix}{2} & & {} \\ {-6} & & {} \\ {} & {} & \end{bmatrix}\text{ And finally this is the last box} \end{gathered}\)one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
Answers
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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O COUNTING AND PROBABILITY Introduction to permutations and combinations Suppose we want to choose 2 colors, without replacement, from the 5 colors red, blue, green, purple, and yellow. (a) How many ways can this be done, if the order of the choices is taken into consideration? X Х ? (b) How many ways can this be done, if the order of the choices is not taken into consideration?
Answers
Answer: We are given five colors, Red Blue Green Purple and Yellow, We need to place them into two, and would like to know the total combinations, A The order matters, B Order does not Matter.
A-The order matters:
\(\begin{gathered} \text{slots =2 } \\ \text{Colors = =5} \end{gathered}\)Therefore we have:
\(5\cdot4\cdot3\cdot2\cdot1=60\cdot2\cdot1=120\text{ ways}\rightarrow\text{ Because order mattered}\)B-The order does not matter:
\(\frac{5!}{2!}=\frac{5\cdot4\cdot3\cdot2\cdot1}{2\cdot1}=60\rightarrow Because\text{ the order does not matter}\)Note!, When the order does matter, we are counting each possibility twice, and when it does not, we only count once.
A car is traveling at a speed of 63 kilometers per hour. What is the car's speed in kilometers per minute? How many kilometers will travel in 5 minutes?
Answers
Answer:
5.25 kilometers
Step-by-step explanation:
63k/60 = 1.05k
1.05k x 5 = 5.25k
The population in a neighborhood increased from 120 to 156 people from 1990 to 1994. Find the rate of change over the intens1990 SI 1994. (1 point)O of a person yes year9 people ger year4 people per year36 people per year
Answers
Step 1: Let's review the information given to us to answer the question correctly:
Initial population = 120 in 1990
Final population = 156 in 1994
Step 2: Let's find the change,in population, this way:
Change in population = Final population - Initial population
Change in population = 156 - 120
Change in population = 36
Step 3: Now, we know the change in population but we need to find the rate.
Rate in population = Change in population/Number of years
Rate in
he triangle on the grid will be translated two units down. On a coordinate plane, triangle A B C has points (2, 1), (0, negative 1), (2, negative 1). Which shows the triangle when it is translated two units down? On a coordinate plane, triangle A prime B prime C prime has points (0, negative 1), (0, negative 3), (2, negative 3). On a coordinate plane, triangle A prime B prime C prime has points (0, 1), (negative 2, negative 1), (0, negative 1). On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 3). On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 1).
Answers
If these coordinates are translated two units down, we will subtract 2 units from the y axis to have A(2, -1), B(0, -3) and C(2, -3)
Translation of coordinate pointTranslation is a transformation technique of changing the position of an object on the xy-plane.
Given the following coordinate of a triangle expressed as:
A(2, 1)
B(0, -1)
C(2, -1)
If these coordinates are translated two units down, we will subtract 2 units from the y axis to have:
A(2, -1)
B(0, -3)
C(2, -3)
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Determine which lines, if any are parallel or perpendicular.
24.
line a: y = 5x - 6
line b: x + 5y = 5
25.
line a: 2x = y = 10
line b: -6x - 3y = 3
line c: x - 2y = 8
Answers
Hence, these lines are perpendicular to each other.
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Draw the graph by using the given equation is
(24)
line \(a: y = 5x - 6\)
line \(b: x + 5y = 5\)
Graph is of the form:-
(25)
line \(a: 2x = y = 10\)
line \(b: -6x - 3y = 3\)
line \(c: x - 2y = 8\)
Graph is of the form:-
Hence, these lines are perpendicular to each other.
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The ratio of dye to pounds of clothing is constant. A worker develops the chart below to show the amount of dye needed for different amounts of clothing.
Clothes Dyeing
Weight of clothing (pounds)
Cups of dye
21
3
42
9
84
12
105
15
For which weight of clothing is the ratio of weight to dye different from the other ratios?
21 pounds
42 pounds
84 pounds
105 pounds
Answers
The weight of clothing is the ratio of weight to dye is different from the other ratios is B. 42 pounds.
How to calculate the ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
It should be noted that from the information given, others have a ratio of 1:7. This is different for 42 pounds since the ratio is:
= 42/9
= 14:3
In conclusion, the correct option is B.
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NEED HELP ASAP WILL GIVE BRAINLIEST
Answers
Answer:
B
Step-by-step explanation:
Set the equation by adding 34 to each side
Use the quadratic formula: x = -b± \(\sqrt{b^2-4ac} \\\) over 2*a
1 =a
-10 = b
34 =c
Insert these values into the quadratic formula
1+4(3x10)-12x equal to -9?And how do you get the answer pls
Answers
Answer: 1+4(30)-12x
1+4*30- 12*x X is equal to 1 so 12x Will be 12
1+4*30-12
5*30-12
150-12
138 so not it dosen't equal 9
Step-by-step explanation: do PEMADS please excuse my dear ant saly
Enter the coordinates of the point
on the unit circle at the given angle.
240°
Answers
EXPLANATION:
To convert degrees to radians, multiply by π / 180 °
since a full circle is 360° or 2π radians.
240°⋅π / 180° radians
Cancel the common factor of 60
4 × π / 3 radians
Combine 4 and π / 3.
4π / 3 radians
HOPE ITS HELPS !!!!!
The coordinates of the points on unit circle at the given angle 240 degrees is\((\frac{-1}{2} ,\frac{-\sqrt{3} }{2} )\)
The formula for calculating Radians is:
\(radians= (degrees)\)×\(\frac{\pi }{180}\)
Formula for calculating coordinates of point (x, y) on circle:x=rcosθ
y=rsinθ (where r is the radius of circle for unit circle r=1)
According to the question
we have
θ = 240 degrees and, r =1
so, 240 degrees = 240×\(\frac{\pi }{180}\)
⇒240 degrees = \(\frac{4\pi }{3}\) (in radians)
Therefore, the coordinates of the points on unit circle at angle \(\frac{4\pi }{3}\) is calculated as
\(x=(1)cos\frac{4\pi }{3}\) (for unit circle r=1)
\(x=\frac{-1}{2}\)
And,
\(y=(1)sin\frac{4\pi }{3}\) (for unit circle r=1)
\(y=\frac{-\sqrt{3} }{2}\)
Hence, the coordinates of the point on unit circle at angle 240 degrees is \((\frac{-1}{2} ,\frac{-\sqrt{3} }{2} )\)
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A rocket is 1 mile above the earth in 30 seconds and 5 miles above the earth in 150 seconds. What is the rockets rate of change in miles per second?
Answers
Given:
At 30 seconds, the distance between the rocket and the earth is 1 mile.
At 150 seconds, the distance between the rocket and the earth is 5 miles.
In the points, (30,1) and (150,5)
To find:
We need to find the rate of change in miles per second.
Explanation:
\(\text{Rate of change =}\frac{y_2-y_1}{x_2-x_1}\)\(\text{Substitute }y_2=5,y_1=1,x_2=150,\text{ and }x_1=30\text{ in the eqaution.}\)\(\text{Rate of change =}\frac{5-1}{150-30}\text{ miles per second}\)\(\text{Rate of change =}\frac{4}{120}\text{ miles per second}\)\(\text{Rate of change =}0.033\text{ miles per second}\)Final answer:
The rocket's rate of change is 0.033 miles per second.