The rate at which the distance between the two cars increased four hours later is 30 mi/h.
How to determine the rate?First of all, we would determine the distances travelled by each of the cars. The distance travelled by the first car after four (4) hours is given by:
Distance, x = speed/time
Distance, x = 24/4
Distance, x = 6 miles.
For the second car, we have:
Distance, y = speed/time
Distance, y = 18/4
Distance, y = 4.5 miles.
After four (4) hours, the total distance travelled by the two (2) cars is given by this mathematical expression (Pythagorean theorem):
z² = x² + y²
Substituting the parameters into the mathematical expression, we have;
z² = 6² + 4.5²
z² = 36 + 20.25
z² = 56.25
z = 7.5 miles.
Next, we would differentiate both sides of the mathematical expression (Pythagorean theorem) with respect to time, we have:
2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt)
Therefore, the rate of change of speed (dz/dt) between the two (2) cars is given by:
dz/dt = [x(dx/dt) + y(dy/dt)]/z
dz/dt = [6(24) + 4.5(18)]/7.5
dz/dt = [144 + 81]/7.5
dz/dt = 225/7.5
dz/dt = 30 mi/h.
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Answer:
30 mi / hr
Step-by-step explanation:
First find out how far the cars are apart after 4 hours
24 * 4 = 96 mi = y
18 * 4 = 72 mi = x
Now use the pythagorean theorem
s^2 = ( x^2 + y^2 ) shows s = 120 miles apart at 4 hours
Now s^2 = x^2 + y^2 Differentiate with respect to time ( d / dt )
2 s ds/dt = 2x dx/ dt + 2y dy / dt
ds/dt = (x dx/dt + y dy/dt)/s
= (72(18) + 96(24)) / 120
ds/dt = 30 mi/hr
Emery borrowed money from her brother to buy a new phone and is paying off a fixed amount each week. After 2 weeks, she will owe $456, and after 5 weeks, she will owe $228.
a. What was the original amount Emery borrowed?
b. How much does she pay each week?
c. How useful are equations in point-slope and slope-intercept forms for answering each question?
The $456 and $228 Emery owed from the amount she borrowed to buy a new phone after 2 weeks and 5 weeks gives;
a. The original amount owed is $608
b. Emery pays $76 each week
c. The point and slope and slope and intercept both gives the amount Emery pays each week as the slope, while the slope and intercept form further gives the original amount borrowed as the y–intercept, c
What is a straight line equation?A straight line equation is one which expresses a linear relationship between variables
Let y represent the original amount of money Emery borrowed from her brother, and let m represent the amount she pays each week to settle the loan, we have;
The given parameters are;
The amount Emery owes after 2 weeks = $456
The amount Emery will owe after 5 weeks = $228
a. The above information can be expressed by writing the following equations;
456 = y - 2•m...(1)
228 = y - 5•m...(2)
Subtracting equation (2) from equation (1) gives;
y - 2•m - (y - 5•m) = 456 - 228 = 228
3•m = 228
Therefore;
m = 228 ÷ 3 = 76
m = 76
The original amount Emery borrowed, y, from equation (1) is therefore;
y = 456 + 2•m
y = 456 + 2 × 76 = 608
The original amount Emery borrowed, y, is $608
b. The amount Emery pays each week, m = $76
c. The straight line equation in point and slope form is presented as follows;
[tex] y_2 - y_1 = m•(x_2 - x_1) [/tex]
From the above equation, the two points (456, 2) and (228, 5) given in the question can be used to find the slope, m, which is the amount paid each month
The slope and intercept form of a straight line equation is y = m•x + c
From the slope and intercept form, we have;
The slope, m = The amount Emery pays per month
The intercept, c = The original amount Emery borrowed
Therefore, both forms of the straight line equation gives the amount Emery pays each week, while the slope and intercept form also gives the original amount Emery borrowed
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1. A piece of power transmission equipment is being designed. The design includesa set of three different meshed gears with a total of 107 teeth between them. If thesecond gear has 13 more teeth than the first gear. The third gear has 15 more teeththan the second gear.How many teeth does the second gear have?
where x is the first, y the second and z the third
the second gear has 13 more teeth than the first gear
[tex]x+13=y[/tex]The third gear has 15 more teeth than the second gear
[tex]y+15=z[/tex]we need solve z form the third equation and solve x from the second equation an replace on the first
[tex]\begin{gathered} z=y+15 \\ x=y-13 \end{gathered}[/tex]replacing
[tex]\begin{gathered} (y-13)+y+(y+15)=107 \\ y-13+y+y+15=107 \\ 3y+2=107 \\ 3y=105 \\ y=35 \end{gathered}[/tex]so, the second gear have 35 teeth
S is the midpoint of segment OU. OS= 7x-9 and SU=4x+3. Determine the length of segment OU.
Answer:
The equation for the value of OU is;
[tex]OU=11x-6[/tex]Explanation:
Given that S is the midpoint of segment OU.
Then;
[tex]OU=OS+SU[/tex]Given in the question;
[tex]\begin{gathered} OS=7x-9 \\ SU=4x+3 \end{gathered}[/tex]Substituting the values of OS and SU to get OU;
[tex]\begin{gathered} OU=OS+SU \\ OU=7x-9+4x+3 \\ OU=7x+4x-9+3 \\ OU=11x-6 \end{gathered}[/tex]Therefore, the equation for the value of OU is;
[tex]OU=11x-6[/tex]given the preimage coordinates complete the translation provide and give the image Coordinates
The coordinates are made up of an x-coordinate and a y-coordinate, written in the form (x, y), the translation given is (x + 1, y - 1), which means adding +1 to all x-coordinates and subtracting -1 to all y-coordinate.
Then, the pair B(0, -4) will be transformed into B'(0 + 1, -4 - 1) → B'( 1, -5)
C( -1, 1) → C' (-1 + 1, 1 - 1) → C'( 0, 0)
D( 1, 3) → D' ( 1 + 1, 3 - 1) → D'( 2, 2)
E( 4, -1) → E' ( 4 + 1, -1 - 1) → E'( 5, -2)
Mrs. Ojo is 5 times older than her son. 3 years ago the product of their ages was 185. How old are they now?
need it now please.
Find the percentage decrease and round to the nearest tenth
Answer:
16.6%
Step-by-step explanation:
First, find the difference between the prices:
$3.95 - $3.45 = $0.50
Then, divide the difference by yesterday's price.
$0.50 ÷ $3.95
≈ 0.166
≈ 16.6%
Answer:
12.7%
Step-by-step explanation:
$3.95 - $3.45 = $.50
$.50 / $3.95 = .127 = 12.7%
Z divided 12 equal 9
Answer:
108
Step-by-step explanation:
12×9=108
just for the extra characters
Answer:
108
Step-by-step explanation:
z/12 = 9
z = 9 × 12
z = 108
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Determine the odds against rolling a 4 on one roll
of a die.
Solution
P(4)=1
6
5
P (fails to roll a 4)=-
6
Answer:
1/6
Step-by-step explanation:
SIX possible rolls 1,2,3,4,5,6
4 is 1 out of 6 or 1/6
The half life of iron-59 is 44.5 days. How much of
a 50g sample would remain after 178 days?
Answer:
If the half-life of a nuclide is 44.5 days, then 178 days is four half-lives.
explanation:
After four half-lives, 0.0625 (0.54) of the original nuclides remains. If 50g is the original mass, then the mass after 4 half-lives is 3.125g.
AT = A0 2(-T/H)
A178 = (50) 2(-44.5/178)
A178 = 3.125
please help and could u give all the steps if there’s more after this thank you so much
Angle IJL is 54 because congruent angles have equal measure.
What are congruent angles?
Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other. The type of angles does not make any difference in the congruence of angles, which means they can be acute, obtuse, exterior, or interior angles.
According to question, angle m IKL = 54
And AB// CD and EF// GH
Angle IKL is alternate interior angle to angle HLK
m angle HLK= m angle IKL (congruent angles have equal measure)
m angle HLK= 54
Similarly, m angle IJL = m angle HLK
Hence, angle IJL= 54
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I have to send you the question
The given expression fro the sum of n terms:
[tex]\begin{gathered} S_n=\frac{n}{2}(a_1+a_n) \\ \text{ Where: }a_1\text{ is the firm term \& }a_n\text{ is the last term} \end{gathered}[/tex]From the given question we have:
[tex]a_1=8,a_n=79,\text{ n =6}[/tex]Substitute these value in the expression of sum of n terms
[tex]\begin{gathered} S_n=\frac{n}{2}(a_1+a_n) \\ S_6=\frac{6}{2}(8+79) \\ S_6=3(87) \\ S_6=3\times87 \\ S_6=261 \end{gathered}[/tex]So, sum of 6 terms is 261
Which of the following lists of data has the largest standard deviation? Hint: you should not need to compute the standard deviation for each list.Select the correct answer below:22, 25, 25, 22, 25, 23, 24, 23, 26, 2413, 11, 11, 11, 10, 14, 14, 10, 11, 1116, 14, 15, 15, 16, 16, 15, 16, 18, 1425, 23, 25, 22, 21, 25, 22, 21, 25, 237, 14, 19, 18, 4, 16, 5, 11, 11, 12
Answer:
7, 14, 19, 18, 4, 16, 5, 11, 11, 12
Explanation:
The standard deviation is a statistic that measures the spread of a dataset relative to its mean.
From the given options, find the range in each of them:
[tex]Range=Highest\;Value-Lowest\;Value[/tex]• Option 1: Range = 26-22=4
,• Option 2: Range=14-10=4
,• Option 3: Range=18-14=4
,• Option 4: Range = 25-21=4
,• Option 5: Range = 19-4=15
We see that the dataset in Option 5 has a far greater range and thus the dataset will have the biggest spread relative to its mean.
Option 5 has the largest standard deviation.
in a 30 16 90° triangle given the short leg equals five find the long leg of the triangle
In a 30-60-90 triangle:
[tex]\begin{gathered} Hypotenuse_{\text{ }}=_{\text{ }}2\cdot short_{\text{ }}length \\ Long_{\text{ }}length=\sqrt[]{3}\cdot short_{\text{ }}length \\ \end{gathered}[/tex]so:
[tex]\begin{gathered} Long_{\text{ }}length=\sqrt[]{3}\cdot5 \\ Long_{\text{ }}length=5\cdot\sqrt[]{3}\approx8.66 \end{gathered}[/tex]Ainsley had 3 yards of string. She used 1/4 yard for a project. She wants to divide the rest into pieces 5/6 yard long. How many pieces can she make?
She can make 3.3 pieces from the remaining length
How to determine the number of pieces to make?From the question, the given parameters are:
Length of string = 3 yardsAmount used for project = 1/4 yardLength of each piece = 5/6 yardWe start by calculating the length of the remaining pieces as a whole
This is calculated as
Length of remaining piece + length used for project = Length of string
Substitute the known values in the above equation
So, we have
Length of remaining piece + 1/4 yard = 3 yards
Subtract 1/4 from both sides
Length of remaining piece = 2.75 yards
The number of pieces is then calculated as
Pieces = Length of remaining pieces/Length of each piece
This gives
Pieces = 2.75 yards/(5/6 yards)
Evaluate the quotient
Pieces = 3.3
Hence, the number of pieces she can make is 3.3
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The formula for the area of a triangle is A = -bh, in which b represents the length of the base and h2represents the height. If a triangle has an area of 115 mm2 and the height is 10 mm, what is the measureof the base?The measure of the base ismm.
The formula for the area of a triangle is A is;
question shown in picture below!!(i only need the 2nd one)
Given the following sequence:
[tex]\mleft\lbrace17,14,11,8,\ldots\mright\rbrace[/tex]notice that the common difference between each term is -3, therefore, we can use the explicit formula for a sequence:
[tex]\begin{gathered} a_n=a_1+(n-1)\cdot d \\ d=-3 \\ a_1=17 \\ \Rightarrow a_n=17+(n-1)(-3) \\ \Rightarrow a_n=17-3n+3=20-3n \\ a_n=20-3n \end{gathered}[/tex]we have that the explicit formula is a_n=20-3n, while the recursive formula is:
[tex]\begin{gathered} a_n=a_{n-1}+d \\ d=-3 \\ \Rightarrow a_n=a_{n-1}-3 \end{gathered}[/tex]help me pleaseeeeeeeeeeeeeeeeeeeeeeeee !!!
Answer:
[tex]f(x)=\frac{5}{6}x+21[/tex]
Step-by-step explanation:
Slope = 5/6
Point = (-18,6)
Using Point-Slope form
y-6=5/6(x+18)
y-6=5/6x+15
y=5/6x+21
:]
I need help with the question above. I took a picture of it.
The answer is: It will be a line.
what is the shape of a cross section that is perpendicular to the basis
If we get the cross section perpendicular to the base of this image, we would get the same shape as the image.
Through the diagram, we can see that if we cut the image to get the cross section perpendicular to its base, we would get the same shape as the image, which is a pentagon.
Roseanne makes 1 1/2 of strawberry lemonade. She pours 1/4 of a liter of lemonade into a thermos to take to the park. Her brother drinks 2/5 of the remaining lemonade. How much lemonade does Roseanne's brother drink? Which expression can be used to determine the amount of lemonade Roseanne's brother drank? A. 1 1/2 - (1/4 x 2/5) B. (1 1/2 + 1/4) x 2/5 C. (1 1/2 - 1/4) x 2/5 D. (1 1/2 - 1/4) ÷ 2/5
we know that
the total lemonade is 1 1/2 liter
She pours 1/4 of a liter of lemonade into a thermos
Her brother drinks 2/5 of the remaining lemonade
the remaining lemonade is equal to
1 1/2-1/4=3/2-1/4=5/4 liters
Multiply by 2/5
(5/4)(2/5)=10/20=1/2 liter
therefore
answer is option
C. (1 1/2 - 1/4) x 2/5
A bag of cookies weighs 19.1 ounces. The bag contains 50 cookies. How much does each cookie weigh?
O2.6 ounces
O 0.3 ounces
O 0.382 ounces
O 3.82 ounces
Answer: 0.382 ounces
Step-by-step explanation:
To find the unit rate of the weight of a single cookie, we will use division.
19.1 ounces per bag / 50 cookies in the bag = 0.382 ounces per cookie
To check our work, we will multiply 0.382 ounces per cookie by 50. Since the bag, with 50 cookies, weighs 19.1 ounces, 0.382 times 50 should equal about 19.1 ounces.
0.382 ounces * 50 cookies = 19.1 ounces ✓
Evaluate: base 6 exponent 0
Answer:
1
Explanation:
Given:
[tex]6^0[/tex]To evaluate the expression above, apply the law of indices below.
[tex]a^0=1,a\neq0[/tex]That is, whenever a number (except 0) is raised to the power of 0, the result is always 1.
Therefore:
[tex]6^0=1[/tex]2 5 4 Q Find the area of the shaded region above.
As you can see in the given figure, there are two different shapes.
One is a rectangle and the other is a triangle.
Recall that the area of a rectangle is given by
[tex]A_R=L\cdot W[/tex]Where L is the length and W is the width.
As you can see from the figure,
W = 4
L = 5
So the area of the rectangle is
[tex]A_R=L\cdot W=5\cdot4=20[/tex]Recall that the area of a triangle is given by
[tex]A_T=\frac{1}{2}\cdot b\cdot h[/tex]Where b is the base of the triangle and h is the height of the triangle.
As you can see from the figure,
b = 4
h = 2
So the area of the triangle is
[tex]A_T=\frac{1}{2}\cdot b\cdot h=\frac{1}{2}\cdot4\cdot2=\frac{1}{2}\cdot8=\frac{8}{2}=4[/tex]Now the total area of the shaded region is the sum of the area of the rectangle and the area of the triangle.
[tex]A=A_R+A_T=20+4=24[/tex]Therefore, the area of the shaded region is 24
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how do I find the given z score
The formula for calculating a z-score is
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where:
*x is the raw score
*μ is the population mean
*σ is the population standard deviation
A native wolf species has been reintroduced into a national forest. Originally 200 wolves were transplanted. After 3 years, the population had grown to 270 wolves. If the population grows exponentially, then at what annual rate is the population growing? Round the answer to the nearest tenth of a percent.
The population is growing at an annual rate of 16.2%
Here, we want to calculate the exponential growth rate
Mathematically, we can write the exponential equation of growth as follows;
[tex]\begin{gathered} P=I(1+r)^t \\ \\ \end{gathered}[/tex]Where P is the population after a certain number of years ( 270 after 3 years
I is the initial popultaion which is 200
r is the percentage we want to calculate
t is the number of yeats to reach P which is 3 in this case
[tex]\begin{gathered} 270=200(1+r)^3 \\ (1+r)^{3\text{ }}\text{ = }\frac{270}{200} \\ \\ (1+r)^3\text{ = 1.35} \\ \\ 1\text{ + r = }\sqrt[3]{1.35} \\ \\ 1\text{ + r = 1.162} \\ \\ r\text{ = 1.162 - 1} \\ \\ r\text{ = 0.162} \end{gathered}[/tex]To the nearest tenth of a percentage, this is 16.2%
if the sum of the first three terms of a GP is half it's sum to infinity. find it's positive common ratio.
Answer:
See below
Step-by-step explanation:
Sum of n = inf = a / ( 1-r) one half of this = 1/2 ( a/(1-r) )
Sum of first 3 terms = a ( 1- r^n) / ( 1-r) = a (1-r^3) / (1-r)
The underlined value are equal ( given in the Q)
1/2 a / (1-r) = a ( 1-r^3) / (1-r) Multiply both side by ( (1-r) )
1/2 a = a ( 1-r^3) divide both sides by a
1/2 = 1- r^3 subtract 1 from both sides
-1/2 = - r^3
1/2 = r ^3
r = cuberoot ( 1/2) = 1/2 ^(1/3) = .793700526
The table shows a proportional relationship.
x 12 8 24
y 3 2 6
Describe what the graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (3, 12).
A line passes through the point (0, 0) and continues through the point (2, 8).
A line passes through the point (0, 0) and continues through the point (6, 24).
A line passes through the point (0, 0) and continues through the point (12, 3).
A graph of which best describes what the proportional relationship would look like is: D. A line passes through the point (0, 0) and continues through the point (12, 3).
What is a graph?In Mathematics, a graph is used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
Additionally, a graph that represents a proportional relationship between two variables would always have a straight line with its data points passing through the origin (0, 0).
Since the graph represents a proportional relationship we have:
Constant of proportionality, k = 12/3 = 8/2 = 24/6 = 4
Ratio = 24:6 = 12:3.
Therefore, (0, 0) and (12, 3) are points on this graph that represents a proportional relationship.
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Answer:d
Step-by-step explanation:trust
Perform the following division and write the quotient in trigonometric form. Write the magnitude in exact form. Write the around it to two decimal places if necessary.8i4 + 5i
SOLUTION
The given complex expression is:
[tex]\frac{-8i}{4+5i}[/tex]Rationalize the denominator
This gives
[tex]\begin{gathered} \frac{-8i}{4+5i}\times\frac{4-5i}{4-5i} \\ =\frac{-32i-40}{16+25} \\ =-\frac{40}{41}-\frac{32i}{41} \end{gathered}[/tex]1. Fiber-Brite could clean 48 rugs in 12 hours. At that rate, how many rugs could Fiber-Brite
clean in 20 hours?
4 thousands +12 hundreds =
Answer:
that's too easy
4 thousands=4000
12 hundreds=120
4000+120=4120
4 thousands and 12 hundreds