Using the Pythagorean Theorem, the rate at which the distance between the vehicles is changing at t = 10 minutes is of -20 km/hour.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the equation given below:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In the context of this problem, the distances of the cars from Sioux Falls, considering the initial distances and the velocities, are given as follows:
Police: P(t) = 60 - 160t.Truck: T(t) = 50 + 140t.The distance after t hours is the hypotenuse of a right triangle in which the legs are the functions, hence:
D²(t) = P²(t) + T²(t).
Hence the rate of change of the distance after t hours is:
2D'(t) = 2P'(t) + 2T'(t)
Simplifying by 2:
D'(t) = P'(t) + T'(t).
Applying the exponent rules, the derivatives are given as follows:
P'(t) = -160.T'(t) = 140.Hence the constant rate is:
D'(t) = -160 + 140 = -20 km/hour.
Meaning that the police car is getting 20 km closer to the truck each hour.
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a spinner contains the numbers 1 through 50. What is the probability that the spinner will land on a number that is not a multiple of 9? Give your answer in fraction form.
Answer:
[tex]\frac{9}{10}[/tex]
Step-by-step explanation:
multiplies of 9, 18,27,36, and 45. Every number has a change to be selected, but these 5. There are 50 numbers
[tex]\frac{50-5}{50}[/tex]
[tex]\frac{45}{50\\}[/tex]
[tex]\frac{9}{10}[/tex]
Use the number line to determine if each number is a solution and type YES or NO . 0 = -10 = 8 = -9 =9 =5 =And don’t worry is just a practice:)
We need to know if the number given belongs to the set or no
0----- YES
-10------ NO
8 ------NO
-9 ----NO
9 ------NO
5 -----YES
In a large school, it was found that 80% of students are taking a math class, 75% of student are taking an English class, and 67% of students are taking both. Find the probability that a randomly selected student is taking a math class or an English class. Write your answer as a decimal, and round to 2 decimal places if necessary. Find the probability that a randomly selected student is taking neither a math class nor an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.
The probability that a randomly selected student is taking a math class or an English class is 0.88
And the probability that a randomly selected student is taking neither a math class nor an English class 0.12
In this question, we have been given in a large school, it was found that 80% of students are taking a math class, 75% of student are taking an English class, and 67% of students are taking both.
Let A represents math class, B represents English class
P(A) = 0.80
P(B) = 0.75
P(A ∩ B) = 0.67
We need to find the probability that a randomly selected student is taking a math class or an English class.
P(A U B) = P(A) + P(B) - P(A ∩ B)
P(A U B) = 0.80 + 0.75 - 0.67
P(A U B) = 0.88
Also, we need to find the probability that a randomly selected student is taking neither a math class nor an English class.
P(~(A U B) ) = 1 - P(A U B)
P(~(A U B) ) = 1 - 0.88
P(~(A U B) ) = 0.12
Therefore, the probability that a randomly selected student is taking a math class or an English class is 0.88
And the probability that a randomly selected student is taking neither a math class nor an English class 0.12
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I'd angle 5=42° and angle 1=117° find the measure of angle CDF.
If angle 5= 42° and angle 1 = 117°
angle CDF = angle 5 + angle 1
=42° + 117°
=159°
The height of a sand dune (in centimeters) is represented by cm, where is measured in years since . Find and , and determine what each means in terms of the sand dune. Give the values of and below, including units.
The height of the sand dune after 13 years is 324 cm. The rate of change height of sand dunes is - 8t.
Given the equation is -
f(t)=1000-4t²
f(13) = 1000 - 4 (13)²
= 1000 - 676
= 324 cm
f'(t) = - 8t
f'(13) = - 8(13)
= -104cm
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Complete Question -
The height of a sand dune (in centimeters) is represented by f(t)=1000-4t2 cm, where t is measured in years since 1995. Find f(13) and f'(13), and determine what each means in terms of the sand dune. Give the values of f(13) and f'(13) below, including units.
if you cant read it, it says : A - is an algebraic expression that continues a variable to power of one - is an example A- is a rational number that is multiplied by aA Variable - is a number that can be written as the ratio fraction of two integers - is the expression - is an example of coefficient - are terms who variables are their exponents are the same one example is an - 7y ( - = blank ) the things you can feel in the blank is 4x, 2y, rational coefficient, like-terms, rational-number , 4, linear expression, and 6x+5
A Linear expression is an algebraic expression that contains a variable to the power of one. 3 + y is an example.
A Coefficient is a rational number multiplied by a variable. A Rational Number is a number that can be written as the ratio, or fraction or intgers.
4 in the expresson 4x is an example of a coefficient.
Like Terms are terms whose variables and their exponent are the same. One example is 9y and -7y
Use the point-slope form to find the equation of each altitude of SABC. (Recall ! a triangle is the perpendicular drawn from any vertex to the opposite side.) (b) A(4,3), B(0,7). C- (a) A(1, -2), B(3,4), C(-2,6)
The rule of the slope of a line has 2 points is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]A = (1, -2), B = (3, 4), C = (-2, 6)
We will take the altitude from A to the opposite side of BC
Then we will find the slope of BC first
x1 = 3 and y1 = 4. point B
x2 = -2 and y2 = 6. point C
We will substitute them in the rule above
[tex]\begin{gathered} m=\frac{6-4}{-2-3}=\frac{2}{-5} \\ m=-\frac{2}{5} \end{gathered}[/tex]The slope of BC = -2/5
Since the product of the slopes of the perpendicular line is -1, then if the slope of one is m, then the slope of the other will be -1/m, we reciprocal it and change its sign, then the slope of the altitude of BC should be 5/2
[tex]m_{\perp}=\frac{5}{2}[/tex]The form of the equation in point-slope is
y - y1 = m(x - x1)
m = 5/2
Since point A is lying on the altitude from A to BC, then
x1 = 1 and y1 = -2 point A
Substitute m and coordinates of point A in the form of the equation above
y - (-2) = 5/2 (x - 1)
[tex]y+2=\frac{5}{2}(x-1)[/tex]The equation of the altitude from A to BC is
y + 2 = 5/2 (x - 1)
x2 + 7x + 12 = ** Show
x² + 7x + 12 = 0
Using the factorisation method
Find two numbers such that its product gives 12 and its sum gives 7
The two numbers are 3 and 4
Replace 7 in the equation by those two numbers and then factorise
That is;
x² + 3x + 4x + 12 = 0
x(x+3) + 4(x+3) = 0
(x+3)(x+4) = 0
Either x+3 = 0 or x+4 =0
Either x = -3 or x= -4
A line that includes the point (1, 10) has a slope of 1. what is its equation in slope-intercept form?
Considering the definition of a line, the equation in slope-intercept of the line that passes through the point (1, 10) and has a slope of 1 is y=x+9.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin.Equation in slope-intercept form in this caseIn this case, you know:
The line has a slope of 1.The line passes through the point (1, 10).Substituting the value of the slope m, the line has a form: y=1x + b or what is the same y=x +b.
Replacing the value of the point in the expression of a linear equation, the value of the ordinate to the origin b can be obtained:
10= 1×1 + b
10= 1 + b
10 -1 = b
9= b
Finally, the equation of the line is y=x +9.
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[tex](a - \frac{95 }{5} )^{2} - \frac{36}{25} m^{2} [/tex]
Please Evaluate
Let's call a year "nice" if its number can be represented as the difference of two powers of two. What is the next nice year? What nice year will be the first one after it?
The next nice year will be 2 nice.
The nice year that will be the first one after it is 4 nice.
What is an exponent?It should be noted that an exponent is used to express the numbers that are either too big or too small. This is usually expressed in their powers.
Fron the information, it as stated that a year is called "nice" if its number can be represented as the difference of two powers of two.
The next nice year will be the difference which will be
= (2² - 2) × nice
= (4 - 2) × nice
= 2 nice.
The one after it will be:
= 2 × 2 nice
= 4 nice.
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a hybrid car can travel 45 miles on one gallon of gas. determine the amount of gas needed for a 500 miles trip
We have the following:
[tex]r=45\frac{m}{g}[/tex]now, for 500 miles
[tex]\frac{500m}{45\frac{m}{g}}=11.11g[/tex]therefore about 11.11 gallons of gas is needed
Answer: roughly 12 gallons or exactly 11.11111111111111111 etc
Step-by-step explanation:
Find the equation of the linear function represented by the table below in slope-intercept form. X у -1 2 -8 5 -17 8 -26 Submit Answer Answer: D attempt 1 out of 2
Slope intercept form:
y = mx + b
m = (y2 - y1)/(x2 - 1) = (-8 - 1)/(2 - (-1)) = -9/(2 + 1) = -9/3 = -3
m = -3
If we take one of the point, for example (2, -8) and use it on the equation with the slope we already found:
y = -3x + b
-8 = -3(2) + b
Solving for b:
-8 = -6 + b
b = -8 + 6 = -2
b = -2
Therefore, the equation is: y = -3x -2
Answer:
y = -3x -2
Solve the equation below and find the variation constant, Find y when x=18, if y varies directly as x, and y=50 when x=13.
Answer:
• k=50/13
,• y=69.231 (to the nearest 1000th)
Explanation:
If y varies directly as x, the equation of variation is:
[tex]y=kx,\text{ k=variation constant}[/tex]When x=13 and y=50
[tex]\begin{gathered} 50=13k \\ k=\frac{50}{13} \end{gathered}[/tex]Substituting k into the equation above, we have:
[tex]y=\frac{50}{13}x[/tex]Therefore, when x=18
[tex]\begin{gathered} y=\frac{50}{13}\times18 \\ y\approx69.231 \end{gathered}[/tex]What is the proportional relationship between a and bA B8. 324 940 15 Write a equation describing the relationship between a and b
Explanation:
A proportional relationship means that the two variables are related by a constant called constant of proportionality:
[tex]a=kb[/tex]k is the constant of proportionality.
To find k we have to use the values of a and b from the table:
[tex]\begin{gathered} k=\frac{a}{b} \\ k=\frac{8}{3} \\ k=\frac{24}{9}=\frac{8}{3} \\ k=\frac{40}{15}=\frac{8}{3} \end{gathered}[/tex]Answers:
• equation: ,a = 8/3 b
,• constant of proportionality:, 8/3
Fowler inc, just paid a dividend of 2.55 per share on its stock. The dividends are expected to grow by 3.9% per year indefinitely. If investers require a 10.4% return on this stock what will the price be in 3 years, what will the price be in 15 years?
When Fowler inc, just paid a dividend, the price in 15 years for the share is $72.36.
How to calculate the price?This will be illustrated as:
P0 = D1 / (Ke - g)
P0 = Current Price
D1 = Expected Dividend after 1 Year
Ke = COst of Equity
g = Growth Rate
Dividend for first year will be:
D1 = D0(1+g)
= $ 2.55 (1+0.039)
= $ 2.55(1.039)
= $ 2.6495
Current price will be:
P0 = D1 / (Ke - g)
= $ 2.6495 / (0.104-0.039)
= $ 2.6495 / 0.065
= $ 40.76
Price in 15 years will be
P15 = D16 / (Ke - g)
P15 = Price after 15 Years
D16 = Expected Div after 16 Years
Ke = COst of Equity
g = Growth Rate
D16 = D0(1+g)^16
= $ 2.55 (1+0.039)^16
= $ 2.55(1.039)^16
= $2.55 * 1.8444
= $ 4.7031
P15 = D16 / (Ke - g)
= $4.7031 / (0.104-0.039)
= $4.7031 / 0.065
= $72.36
The price is $72.36
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The wheels on noah’s bike have a circumference of about 5 feet how many time do the wheels rotated if noah rides 40 feet
A hiker began hiking from the 0-mile mark of a trail. The hiker walked at a steady rate of 214 miles per hour. Which diagram best represents this information?
The diagram which best represents the hiking track of the hiker is attached below.
As time increases, speed is constant, i.e., 214 miles per hour
So, the distance increases with an increase in time.
Speed = Distance/Time
Let, Distance = D and Time = T,
214 = D / T
D = 214T
Let, D = Y coordinate, Time = X coordinate
y = 214 x→→Equation of the line passing through the origin and slope 214.
For the given situation, the equation is a linear equation and the equation will be on the y-axis.
Hence, a diagram that represents this information is:
Correct question :
A hiker began hiking from the 0-mile mark of a trail. The hiker walked at a steady rate of 214 miles per hour. Draw the diagram which best represents this information?
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Line c has an equation of y = -5x + 3. Parallel to line c is line d, which passes through the
point (2, -6). What is the equation of line d?
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient so equation of line d is y = -5x + c.
Substitute (2,-6) into the equation to find c.
-6 = -5(2) + c
c = 4
Hence equation of line d is y = -5x + 4.
Assume that a sample is used to estimate a population mean μ
. Find the margin of error M.E. that corresponds to a sample of size 22 with a mean of 69.3 and a standard deviation of 8.6 at a confidence level of 95%.
Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.
M.E. =
Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
The margin error M.E. that corresponds to a sample of size 22 with a mean of 69.3 and a standard deviation of 8.6 at a confidence level of 95% is 0.04694
We would utilize the t distribution in the estimation of the margin of error because the population standard deviation is unknown (and the sample size is less than 30).
Error margin = t-critical * standard deviation/square root sample size
It is given in the above question that,
Standard deviation is given as = 8.6
And, the Sample size which is given is = 22
Also, the confidence level which given is = 95%
Then the alpha will be = 100% - 95%
= 5% = 0.05
Now, the critical value, t would be = alpha / 2
= 0.05 /2 = 0.025
Also, the sample we'll consider will be = given sample size - 1 = 22 -1 = 21
To find the margin error, we'll put all the values in the formula
Error margin = t-critical * standard deviation/square root sample size
= [tex]\frac{0.025 * 8.6}{\sqrt{21} }[/tex]
= 0.215 / 4.58
= 0.04694
Hence, the margin error M.E. that corresponds to a sample of size 22 with a mean of 69.3 and a standard deviation of 8.6 at a confidence level of 95% is 0.04694
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Why the answer to 12am=4, for a is a=1/3m help please
We can solve the given expression for [tex]a=\frac{1}{3m}[/tex] by using the division method.
The given expression is [tex]12am=4[/tex].
We have to solve the given expression for [tex]a=\frac{1}{3m}[/tex].
Now we solving the expression.
[tex]12am=4[/tex]
We can easily solve the expression by seeing the value that we have to solve.
We using the division method to solve the given expression.
In the division method we divide the both side by same variable to find to value of particular variable.
For solving the expression for [tex]a[/tex] we eliminate [tex]12m[/tex].
We divide the given expression by [tex]12m[/tex] on both side
[tex]\frac{12am}{12m}=\frac{4}{12m}\\a=\frac{4}{3\times4m}\\a=\frac{1}{3m}[/tex]
Now we solve the given expression for [tex]a=\frac{1}{3m}[/tex].
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Independent Practice7. The original quantity is 10 and the new quantityis 13. What is the percent change? Is it anincrease or decrease?8. The original quantity is 5 and the new quantityis 3. What is the percent change? Is it an increaseor decrease?7%1310100%100%poP.P Р-P%.The percent increase is%The percent decrease is
The percentage increase or decrease can be calculated by :
[tex]\%change=\frac{New-Orig}{Orig}\times100[/tex]7. New = 13, Orig = 10
% change = [(13 - 10)/10] x 100 = 30% (Increase)
8. New = 3, Orig = 5
% change = [(3 - 5)/5] x 100 = -40% or 40% (decrease)
Given the recursive formula below, what are the first 4 terms of the sequence? A) 17, –6, –3, 0B) 17, 13, 9, 5C) 17, 19, 21, 23D) 17, 15, 13, 11
Explanation
Step 1
we have the recursive formula
[tex]f(x)=\begin{cases}f(1)=17 \\ f(n)=f(n-1)-2\text{ if n }>1\end{cases}[/tex]A recursive formula is a formula that defines each term of a sequence using the preceding term(s), we can see in the formula that the new term ( f(n)) equals the previous term minus 2
so
[tex]\begin{gathered} f(1)=17 \\ hence \\ f(n)=f(n-1)-2 \\ \text{for n=2} \\ f(2)=f(2-1)-2 \\ f(2)=f(1)-2 \\ f(2)=17-2=15 \\ so,\text{ the second term is 15} \end{gathered}[/tex]and so on,
Now for n=3
[tex]\begin{gathered} f(n)=f(n-1)-2 \\ f(3)=f(3-1)-2 \\ f(3)=f(2)-2 \\ f(3)=15-2=13 \\ so,the\text{ second third terms i s13} \end{gathered}[/tex]for n=4
[tex]\begin{gathered} f(n)=f(n-1)-2 \\ f(4)=f(4-1)-2 \\ f(4)=f(3)-2 \\ f(4)=13-2=11 \\ \text{hence, the fourth term is 11} \end{gathered}[/tex]so, the answer is
D) 17,15,13,11
I hope this helps you
5. The following stem-and-leaf plots compare the ages of 30 actors and 30 actresses at the time they won the Oscar award for Best Actor or Actress.ActorsStemsActresses2146667987532213001133444557788877654332210041112966515210601167480(a) What is the age of the youngest actor to win an Oscar? years(b) What is the age difference between the oldest and the youngest actress to win an Oscar? years(c) What is the oldest age shared by two actors to win an Oscar? years
Answer:
(a) 31 years
(b) 59 years
(c) 56 years
Step-by-step explanation:
In general, when reading a stem and leaf plot, we read firstly the number in the steam (middle) and then in the leaf.
Now, let's move on to the question:
(a) As we can see in the graph, the youngest actor has 31 years.
(b) The youngest actress is 21 years old and the oldest is 80.
So, the difference is 80 - 21 = 59 years.
(c) In this exercise, we have to look for actors who had the same age. That means, when evaluating the steam, we will have to find similar values in the leaf. The oldest age shared is 56 years.
7. Which state had a population of eight
hundred four thousand, one hundred
ninety-four?
Answer:
I read it's south Dakota but not sure of it.
I found it from this picture
Question
Solve.
−6.6x=−4
What is the solution to the equation?
Enter your answer as a simplified fraction in the box.
The solution to the equation would be 20/33 as a simplified fraction.
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of that variable would give a true mathematical statement.
We have been given an equation as; −6.6x=−4
Thus we need to solve the equation to find the solution.
-6.6x = -4
Then Divide both sides by -6.6.
x = -4/(-6.6)
x = 40/66
x = 20/33
Hence, the solution to the equation would be 20/33 as a simplified fraction.
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A travel agent arranged a payment plan for a client. It required a down payment of $150 and 15 monthly payments of $657. What was the total cost of the plan?
Answer:
$10,005
Step-by-step explanation:
We need to find the total cost of the plan and we already know that the client need to pay $150 for downpayment and 15 monthly payments of $657.
So all we need to find is the 15 monthly payments of $657. (Which we could found with multiplying $657 with 15)
$657×15 = $9,855
Now we just add it with the downpayment ($150) to find the total cost of the plan.
$9,855+$150 = $10,005
You could write the steps like this:
$150+($657×15)=$10 005
Cameron Benson is a dental assistant.
He earns $11.17 per hour and time
and a half for overtime. Last week
he worked 40 hours plus 7 hours of
overtime.
please help tutor I will give you a good rating
Answer
Options A, D and E are correct.
The two functions are increasing.
The function for plan II has a greater unit rate.
The function for plan I has a greater y-intercept.
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
For the first plan, there's a one time investment of 15,000 dollars and subsequent monthly payments of 500 dollars.
y = 15,000 + 500x
y = 500x + 15,000
Slope = unit rate of increase = 500
y-intercept = 15,000
For the second plan, the function is just given as
y = 12,000 + 520x
y = 520x + 12,000
Slope = unit rate of increase = 520
y-intercept = 12,000
We can see that
The two functions are increasing.
The function for plan II has a greater unit rate.
The function for plan I has a greater y-intercept.
Hope this Helps!!!
Match each compound inequality on the left to the graph that represents its solution on the right. 4x + 3 > 15 or -6x > 12 -5 0 1 - 8x > - 24 and -10 < 2x - 6 -7 1 - 29 < 9x - 2 < 16 6 4
The first compound inequality 4x+3>15 or -6x≥12 matches the third graph, i.e x>3 or x≥-2.
The second compound inequality -8x>-24 and -10≤2x-6 matches the second graph, i.e x>3 or x≥-2.
The third compound inequality -29≤9x-2<16 matches the first graph, i.e -3≤x<2.
Given the expressions are:
a. 4x+3>15 or -6x≥12
simplify.
4x+3>15 or -6x≥12
4x>15-3 or x≥12/-6
4x>12 or x≥-2
x>3 or x≥-2
hence the graph is third.
b. -8x>-24 and -10≤2x-6
simplify.
-8x>-24 and -10≤2x-6
x>-24/-8 and -10+6≤2x
x>3 and -4≤2x
x>3 and -4/2≤x
x>3 and -2≤x
x>3 and x≥-2
hence the second graph matches.
c. -29≤9x-2<16
first take -29≤9x-2
simplify
-29+2≤9x
-27≤9x
-27/9≤x
-3≤x
now take 9x-2<16
simplify.
9x<16+2
9x<18
x<18/9
x<2
hence we get -3≤x<2
hence the first graph matches the given inequality.
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Use ''compound inequality'' in the main answer and ''graph'' in the explanation.