Answers
Answer: the estimated maintenance cost of cars when the age of cars is 12 years is 16.5 ( in 100 birr)
Step-by-step explanation:
To obtain the regression equation for costs related to age of cars, we can use the method of least squares. This method involves finding the line of best fit that minimizes the sum of the squared differences between the predicted values and the actual values.
The equation for a linear regression line is:
y = a + bx
where a is the y-intercept and b is the slope of the line.
To find the slope of the line (b), we can use the formula:
b = (n(∑xy) - (∑x)(∑y)) / (n(∑x^2) - (∑x)^2)
To find the y-intercept (a), we can use the formula:
a = (∑y - b(∑x)) / n
Given the data provided, we can calculate the following values:
∑x = 142
∑y = 150
∑xy = 2430
∑x^2 = 10304
n = 8
By substituting these values into the formulas for b and a, we can find the slope and y-intercept of the line:
b = (8(2430) - 142(150)) / (8(10304) - 142^2) = 0.5
a = (150 - 0.5(142)) / 8 = 13.5
Therefore, the regression equation for the costs related to age of cars is:
y = 13.5 + 0.5x
To estimate the maintenance cost of cars when the age of cars is 12 years, we can substitute x = 12 into the equation and solve for y:
y = 13.5 + 0.5(12) = 16.5
So the estimated maintenance cost of cars when the age of cars is 12 years is 16.5 ( in 100 birr)
Related Questions
NO LINKS!!! NOT MULTIPLE CHOICE!!!
Find a counterexample to show that the following conjectures are false:
a. The sum of two numbers is always greater than zero.
b. The sum of a positive number and a negative number is always positive.
c. If a figure has four sides, then it is a rectangle.
Answers
Answer: a. The sum of two numbers is always greater than zero.
Step-by-step explanation:
A counterexample to this conjecture would be when the two numbers are both negative. For example, the sum of -5 and -3 is -8, which is less than zero.
b. The sum of a positive number and a negative number is always positive.
A counterexample to this conjecture would be when the negative number is greater than the positive number. For example, the sum of 5 and -6 is -1, which is less than zero.
c. If a figure has four sides, then it is a rectangle.
A counterexample to this conjecture would be a square. A square has four sides, but it is not a rectangle because all of its angles are 90 degrees while a rectangle has four right angles.
It's good to keep in mind that a conjecture is a statement that is made based on observations and that it hasn't been proven yet, therefore a counterexample can be used to show that the conjecture is false.
Answer:
a) -5 + 1 = -4
b) 2 + (-10) = -8
c) A scalene trapezium.
Step-by-step explanation:
A counterexample is proof that a conjecture is false.
Part aGiven conjecture:
The sum of two numbers is always greater than zero.If one of the numbers is negative, and its absolute value is equal to or greater than the value of the positive number, the result will always be equal to or less than zero.
Counterexample:
-5 + 1 = -4As -4 is less than zero, this proves that the conjecture is false.
Part bGiven conjecture:
The sum of a positive number and a negative number is always positive.If the absolute value of the negative number is greater than the value of the positive number, the result will always be negative.
Counterexample:
2 + (-10) = -8As -8 is negative, this proves that the conjecture is false.
Part cGiven conjecture:
If a figure has four sides, then it is a rectangle.Counterexample:
A scalene trapezium.The interior angles of a rectangle are congruent (90°).
A scalene trapezium has four sides, but as its interior angles are all different, it is not a rectangle. This proves that the conjecture is false.
Toby has a strawberry lace that is 36 cm long ar He needs pieces 18 mm long to decorate a cake. How long is the lace in mm? How many 18 mm pieces can he cut from the lace? help⭐⭐⭐⭐⭐
Answers
Answer:
The lace is 36 cm long and 1 cm = 10 mm. So, 36 cm = 360 mm.
He can cut the lace into 18 mm pieces, so he can cut 360 mm / 18 mm = 20 pieces of 18 mm lace from the 36 cm lace.
Please look at the picture and answer the question thank you
Answers
Answer:
f(-4) = -36
Step-by-step explanation:
Step-by-step explanation:
A function assigns the value of each element of one set to the other specific element of another set. The value of the function when the value of x is -4 is 92.
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
Given that F(x)=3x²-10x+4, therefore, the value of the function can be calculated by substituting the value of x as -4.
Therefore, the value of the function when the value of x is -4 can be calculated as shown below,
F(x) = 3x² - 10x + 4
F(-4) = 3(-4)² - 10(-4) + 4
= 3(16) + 40 + 4
= 48 + 40 + 4
= 92
Hence, the value of the function when the value of x is -4 is 92.
Amanda is playing a role-playing game with her friends. She will roll dice to determine if her character unlocks a treasure chest. The probability of her
13
character unlocking the treasure chest is
Find the odds in favor of her character unlocking the treasure chest.
Answers
The odds in favor of Amanda unlocking the treasure chest is 1/5.
We have to find the odds in favor of Amanda's character unlocking the treasure chest. Odds in favor is the ratio of the number of favorable outcomes to the number of unfavorable outcomes.
[tex]P (A) = \frac{no.of favorable outcomes}{no. of unfavorable oucomes}[/tex]
P(A), is used to denote the probability of the event A.
Before finding out the odds in favor, we need to find the probability of her unlocking the treasure chest {P(T)}
Total no. of outcomes = 6 (as a dice has 6 sides)
Number of outcomes desired = 1 (that unlocks the treasure chest)
Therefore, the probability of unlocking the treasure chest
P(T) = Number of outcomes desired/ Total no. of outcomes = 1/6
P(T) is our favorable outcome.
Any other outcome would be unfavorable,
Therefore, the number of unfavorable outcomes would be
= Total no. of outcomes - number of the desired outcomes = 6-1 = 5
Thus, applying the formula for P(A)
P(A) = no. of favorable outcomes/ no. of unfavorable outcomes
= 1 / 5 (Ans)
Thus, the odds in favor of Amanda unlocking the treasure chest is 1/5.
Learn more about probability
https://brainly.com/question/30034780
Marco budgets $1,600 a month for expenses.
According to the graph, how much does he pay
for his credit card, groceries, and rent?
$1,008
$908
$1,142
$1,029
Answers
Marco pays $64 for credit card, $272 for Groceries and $672 for rent
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Marco budgets $1,600 a month for expenses.
According to the graph he pays 4% of credit card
Now let us find 4% of 1600
4/100×1600
0.04×1600
$64 Marco pays for credit card.
From graph, he pays 17% for groceries
17% of 1600
17/100×1600
0.17×1600=$272
$272 Marco pays for Groceries.
From graph, he pays 42% for rent
42/100×1600
0.42×1600=672
$672 Marco pays for Rent.
Hence, Marco pays $64 for credit card, $272 for Groceries and $672 for rent
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ1
Square ABCD has a diagonal AC with the given vertices. Find the coordinates of the remaining vertices.
A(-4,-1) and C(2,5)
The coordinates are ( , ) and ( , )
Answers
Answer: To find the coordinates of the remaining vertices of square ABCD, we can use the information we have been given about the diagonal AC and its vertices. The diagonal AC has been given as having the vertices A(-4, -1) and C(2, 5). Since a square has right angles, we know that the other two vertices of the square must form a right angle with the diagonal AC.
To find the coordinates of vertex B, we know that it must have the same y-coordinate as vertex A, but a different x-coordinate. Since the x-coordinate of vertex A is -4, we can deduce that the x-coordinate of vertex B must be the same as the x-coordinate of vertex C, which is 2. Therefore, the coordinates of vertex B are (2, -1).
To find the coordinates of vertex D, we know that it must have the same x-coordinate as vertex A, but a different y-coordinate. Since the y-coordinate of vertex A is -1, we can deduce that the y-coordinate of vertex D must be the same as the y-coordinate of vertex C, which is 5. Therefore, the coordinates of vertex D are (-4, 5).
In summary, the coordinates of the remaining vertices of square ABCD are B(2, -1) and D(-4, 5)
Step-by-step explanation:
Help pls simplify the following expression (attached to image )
Answers
Answer:
[tex]\frac{1}{343}[/tex]
Step-by-step explanation:
[tex]7^{-3}[/tex] = [tex]\frac{1}{7^{3} }[/tex] = [tex]\frac{1}{7x7x7}[/tex] = [tex]\frac{1}{343}[/tex]
here are 15 European cities that Yolanda would eventually like to visit. On her next vacation, though, she only has time to visit 3 of the cities: one on Monday, one on Tuesday, and one on Wednesday. She is now trying to make a schedule of which city she'll visit on which day. How many different schedules are possible? (Assume that she will not visit a city more than once.)
Answers
The number of different schedules are possible is given by the permutation and the equation is P = 2,730 schedules
What are Permutations?A permutation is an ordered arrangement.
The number of ordered arrangements of r objects taken from n unlike objects is:
Permutation ⁿPr = n! / ( n - r )!
Given data ,
Let the total number of schedules be P
Let the total number of European cities be n = 15
Let the number of cities Yolanda can visit in time r = 3 cities
So , the total number of different schedules is calculated by permutation and ,
The total number of different schedules = ⁿPr = n! / ( n - r )!
Substituting the values in the equation , we get
¹⁵P₃ = ( 15 ) ! / ( 15 - 3 ) !
¹⁵P₃ = ( 15 ) ! / ( 12 )!
¹⁵P₃ = 15 x 14 x 13
¹⁵P₃ = 2,730 schedules
Hence , the value of P is 2,730 schedules
To learn more about permutations click :
https://brainly.com/question/1216161
#SPJ1
A snack mix recipe calls for 2
1
4
cups of chips and
1
5
cup of dip.
Xander wants to make the same recipe using 1 cup of dip. How many cups of chips will Xander need?
Answers
i do not know the answer either
Find The Missing Number
1. 1:2=4N
2: 3:8=N:16
3.15:20=30:N
4.N:25=2:5
5.10:N=40:80
Answers
The missing number of all the ratios are given below.
What is ratio?The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
The ratios are given.
1. 1:2=4:N
2: 3:8=N:16
3.15:20=30:N
4.N:25=2:5
5.10:N=40:80
p:q can be written as p/q.
To find the missing number:
1. 1:2=4:N
1/2 = 4/N
So, N = 8
2: 3:8=N:16
So, N = 6
3.15:20=30:N
So, N = 40
4.N:25=2:5
So, N = 10
5.10:N=40:80
N = 20
Therefore, all the missing numbers are given above.
To learn more about the ratio;
https://brainly.com/question/13419413
#SPJ1
Verify that [n+3]!\n!=(n+1
Answers
Answer:
To verify that [n+3]! / n! = (n+1), we can use the definition of factorial:
[n+3]! = (n+3) * (n+2) * (n+1) * n!
And we can cancel out n! from both sides of the equation:
(n+3) * (n+2) * (n+1) = n+1
Which is true, and thus [n+3]! / n! = (n+1) holds true.
Another way to verify this is by simplifying the RHS and LHS
(n+1) = (n+1)
And the LHS,
(n+3)! = (n+3)(n+2)(n+1)n! = (n+1)(n+2)(n+3)n! = (n+1)(n+2)(n+3)!/n!
which is also equal to (n+1)
So, [n+3]! / n! = (n+1) is true.
2. Kasie lives in Seattle. She can see her house from the observation deck of the Seattle Space Needle. The
observation deck is 520 feet above the ground and the angle of depression from the deck to her house
is 70. What is the direct distance from the base of the Space Needle to Kasie's house? Round your
answer to the nearest foot.
Answers
Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.
What is angle of depression?The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.
Given,
Height of the observation deck AB = 520 feet
Angle of depression = 70°
Distance of the Space needle base to house BC = ?
By the figure,
tan70° = AB/BC
BC = tan70°(AB)
BC = 2.7475(520)
BC = 1428.7 feet
Distance of the Space needle base to house to nearest foot = 1429 feet
Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.
Learn more about angle of depression here:
https://brainly.com/question/13514202
#SPJ1
which graph represents the function y=-2cos(2πx)
Answers
Answer:
Step-by-step explanation:
When it comes to graphing a trigonometric function we use the amplitude, period, vertical shift and these values all help our graph come together to give us our final answer.
In this case,
The amplitude=2
period=1
and there is no phase / vertical shift.
Caitlyn wants to determine what percent of her trail mix is chocolate pieces, so she counts out exactly how many eacch item are in her bag. There are 28 raisins 28 chocolate pieces and 24 peanuts what percent of pieces in the trail mix are chocolate?
Answers
well, there are 28 + 28 + 24 = 80 pieces total, or namely that's the 100%, and we know that 24 of those are chocolates
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 80 & 100\\ 24& x \end{array} \implies \cfrac{80}{24}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 10 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 10x=300\implies x=\cfrac{300}{10}\implies x=30[/tex]
To figure out what percentage of the trail mix is chocolate, we add up all the pieces, divide the number of chocolate pieces by the total and multiply by 100. In this case, we find that 35% of the trail mix is chocolate.
Explanation:In order to figure out the percent of chocolate pieces in Caitlyn's trail mix, we first need to determine the total number of pieces. Caitlyn counts 28 raisins, 28 chocolate pieces, and 24 peanuts, which gives us a total of 80 pieces in the mix. Then, since there are 28 chocolate pieces, we divide 28 (chocolate pieces) by 80 (total pieces). This will give us the decimal representation of the portion of the mix that is chocolate. To convert this into a percentage, we multiply by 100. Hence, the calculation will be (28/80)*100 = 35%. So, 35% of the trail mix is chocolate.
Learn more about Percent Calculation here:https://brainly.com/question/34428429
#SPJ2
Oreana's 150 g bag of trail mix is x% raisins. Brandon's 250 g bag of trail mix is y% raisins. They combine the two mixes together in one bowl.
Write an expression which shows how many grams of raisins are in the bowl
Answers
The expression which shows how many grams of raisins are in the bowl will be
(0.01x) * 150 + (0.01y) * 250
What is the expression that shows the raisin?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The expression which shows how many grams of raisins are in the bowl will be:
= (x% × 150) + (y% × 250)
= (0.01x) * 150 + (0.01y) * 250
This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.
Learn more about expressions on:
https://brainly.com/question/723406
#SPJ1
At an amusement park, only 17 people are allowed on a ride at the
same time. There are 157 people waiting in line. How many groups
of riders will there be?
Show your work.
Answers
Answer:
To find out how many groups of riders there will be, we need to divide the total number of people waiting in line (157) by the maximum number of people allowed on the ride at one time (17).
157 people / 17 people/group = 9.235 groups (approx)
But since the groups must be in whole numbers, we have to round up the value 9.235 groups to the next whole number, which is 10 groups.
So, the number of groups of riders will be 10.
Answer: 9 groups of riders.
Step-by-step explanation:
To find out how many groups of riders there will be, you need to divide the total number of people waiting in line by the maximum number of people allowed on the ride at one time.
157 (total people in line) ÷ 17 (people allowed per ride) = 9.235 (groups of riders)
Because you can't have a fraction of a group, you need to round down to get the whole number of groups.
So the answer is 9 groups of riders.
 Using the Distributive Property as a good first step to solving the equation, you could simplify to get which of these choices?
7(5x + 2) = -4(6 - 5x)
0
à
Ib
0
O
0
d
e
35x + 14 = -24 - 20x
35x + 14 = -24 + 20x
5x + 14 = 6 + 20x
35x + 2 = -24 - 5x
35x + 2 = 24 - 20x
Answers
answer would be b
a car is travelling at 18.1m/s with a constant acceleration of 3.7m/s^2. the car is attempting to pass a truck which is moving at a constant velocity of 29.7m/s. how far in meters must the car travel until it matches the trucks velocity
Answers
Answer:
Step-by-step explanation:
?
The car must travel a distance of 130.7 meters. This can be determined by using the equation for distance travelled with a constant acceleration:
Distance = Initial Velocity x Time + (1/2) x Acceleration x Time^2
In this case, the initial velocity is 18.1m/s, the acceleration is 3.7m/s^2, and the final velocity is 29.7m/s. We can set the final velocity equal to the initial velocity and solve for time:
29.7m/s = 18.1m/s + 3.7m/s^2 x Time
Time = 5.4 seconds
We can then plug this value for time into the equation for distance:
Distance = 18.1m/s x 5.4s + (1/2) x 3.7m/s^2 x 5.4s^2
Distance = 130.7 meters
Please help me with this question.
Answers
The matrix products are given as follows:
a. AB = [58 -6 24]
[18 63 45]
[-22, -39, -33]
b. BA = [32 -26]
[10 56]
The addition A + B is not possible to obtain, the matrices have different dimensions.
How to multiply the matrices?The dimensions of each matrix are given as follows:
A = 3 x 2.B = 2 x 3.Hence the dimensions of each product are given as follows:
AB = 3 x 3.BA = 2 x 2.To multiply matrices, the rows of the first are multiplied by the columns of the second, hence matrix AB is obtained as follows:
Row 1, column 1: -7(-6) + 4(4) = 58.Row 1, column 2: -7(-2) + 4(-5) = -6.Row 1, column 3: -7(-4) + 4(-1) = 24.Row 2, column 1: -9(-6) - 9(4) = 18.Row 2, column 2: -9(-2) - 9(-5) = 63.Row 2, column 3: -9(-4) - 9(-1) = 45.Row 3, column 1: 7(-6) + 5(4) = -22.Row 3, column 2: 7(-2) + 5(-5) = -39.Row 3, column 3: 7(-4) + 5(-1) = -33.Hence the matrix AB is given as follows:
AB = [58 -6 24]
[18 63 45]
[-22, -39, -33]
Matrix BA is obtained as follows:
Row 1, Column 1: -6(-7) - 2(-9) - 4(7) = 32.Row 1, Column 2: -6(4) - 2(-9) - 4(5) = -26.Row 1, Column 1: 4(-7) - 5(-9) - 1(7) = 10.Row 1, Column 2: 4(4) - 5(-9) - 1(5) = 56.Hence the matrix BA is given as follows:
BA = [32 -26]
[10 56]
More can be learned about multiplication of matrices at brainly.com/question/24274686
#SPJ1
The rule C=6.3r gives the approximate circumference C of a circle as a function of its radius r. Identify the independent and dependent variables in this relationship. Explain your reason.
Answers
Answer:
below
Step-by-step explanation:
The INdependent variable is 'r'
'C' DEPENDS on the value of 'r'...it is the dependent variable
A diagram of a roundabout that is being designed to improve driver safety on a busy road is shown. The radius of the circular field planned for landscaping is 27.5 feet. What is the approximate distance around the outside of the circular field? PLEAS HELP WANT!
A. 345.4 feet
B. 172.7 feet
C. 86.35 feet
D. 2,323.1 feet
Answers
The approximate distance around the outside of the circular field is B. 172.7 feet.
Length of the circumference of a circle.A circumference is the part of a circle which is referred to as the boundary. The length of the circumference of a circle is given as;
length of a circumference = 2πr
where r is the radius of the circle.
To determine the distance around the outside of the circular field, we have;
length of the distance around the outside of the circular field = 2πr
given that;
r = 27.5 feet
length of the distance around the outside of the circular field = 2πr
= 2*(22/ 7)*27.5
= 172.7
The length of the distance around the outside of the circular field is 172.7 feet.
Learn more about the length of the circumference of a circle at https://brainly.com/question/20489969
#SPJ1
Hectors school is holding a fitness challenge
Answers
Answer: What is the question ?
Step-by-step explanation:
Answer: 2 7/8 hours per week
hectors rate is greater
Step-by-step explanation:
-2x+13<-3 please answer it in a inequality notation and number line
Answers
Answer:
x<4
Step-by-step explanation:
_2*+13<_3 take-13 crossing the less sign acting same as equal then with number line, at point 13 go 3 steps to the left to get -16 then divide it by-2 to get x<4
Jenny drew a figure in art class. Does it have rotational symmetry? If yes, what is the angle of rotation.
Answers
Answer : Yes, it has rotational symmetry. The angle of rotation is, 60 degree.
What is Rotational symmetry?It is a shape that has Rotational Symmetry when it still the same after the rotation.
here, we have,
The given figure is hexagon and it has rotational symmetry because it still the same after the rotation.
As there are 6 sides of hexagon geometry and the degree of rotation is, .
So, the angle of rotation = 360/60
=60 degree
To learn more on rotational symmetry click:
https://brainly.com/question/14324972
#SPJ1
After school Sasha likes to make snack by mixing raisins and nuts in the ratio 3:5 when she checked cupboard today there were only 60g of raisins and 75g of nuts left.what is the largest snack sasha can make while still using the correct ratio of ingredients
Answers
The largest snack Sasha can make while still using the correct ratio of ingredients is 555g.
What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given that after school Sasha likes to make snacks by mixing raisins and nuts in a ratio of 3:5 when she checked the cupboard today there were only 60g of raisins and 75g of nuts left.
The largest snack Sasha can make while still using the correct ratio of ingredients is calculated as,
E = ( 60 x 3 + 75 x 5 )
E = 180 + 375
E = 555 g
To know more about ratios and proportions follow
https://brainly.com/question/2914376
#SPJ1
Show me you work!
Subtract: 2 1/4 - 1 2/3 =
A) 1 7/12
B) 1/3
C) 5/12
D) 7/12
Answers
Answer:
D) 7/12
Step-by-step explanation:
The first thing we want to do is find a like denominator for the fraction
Both 4 and 3 go into the multiple 12, so we'll use that
4x3=12
3x4=12
and what you do to one side, you must do to the other so we have
1/4x3= 3/12
2/3x4= 8/12
With that you get 2 3/12 and 1 8/12, which is subtractable
Take one from 2 so that you can make 3/12 15/12
15/12-8/12=7/12
This gives us our answer 7/12
Hope this helps! Please rate brainliest!!!
Don't worry, I gotchya bro :)
2 1/4 - 1 2/3
2 1/4 to an improper fraction is 9/4
1 2/3 to an improper fraction is 5/3
to get the same denominator multiply 9/4 by 3 and 5/3 by 4.
27/12 - 20/12
7/12 IS YOUR ANSWER.
Note: This took my time, brain, and eyes to help. If you can just click one button of brainliest that would mean somthing.
Un numeral aumentado en el triple de su cifra de decenas resulta 93. Hallar la suma de sus cifras
Answers
El número de este problema es 72, y la suma de sus cifras da 9.
¿Como hallar la suma de sus cifras?En este problema tenemos un numero de dos cifras, que podemos escribir como:
a*10 + b
Donde a y b son numeros enteros entre 0 y 9, y son las cifras de nuestro número.
Sabemos que si a este número le aumentamos 3 veces la cifra de decenas, resulta en 93, entonces podemos escribir:
a*10 + b + 3*a = 93
a*13 + b = 93
Ok, ahora simplemente devemos reemplazar los valores de b por numeros enteros y resolver la ecuación para a, asi hasta que el resultado de a tambien de un numero entero.
si b = 5
a*13 + 5 = 93
a*13 = 93 - 5
a*13 = 88
a = 88/13 = 6.7
No es una solucion.
si b = 2
a*13 + 2= 93
a*13 = 93 - 2
a*13 = 91
a = 91/13
a = 7
Esta es la solución.
Las cifras son a = 7 y b = 2, y su suma da:
7 + 2 = 9
Aprende más sobre números enteros:
https://brainly.com/question/17695139
#SPJ1
A whale-watching tour boat, moving west at a constant speed 45 miles per hour, has finished viewing a whale and is returning to shore. One whale that is right next to the boat swims away in the opposite direction, moving at a constant speed of 25 miles per hour. They swim apart for 35 minutes and then change direction. The boat turns south and again the whale turns in the opposite direction of the boat. They continue moving apart for another 25 minutes. How far apart are the boat and the whale? (Round your answer to the nearest mile).
Answers
The boat and the whale are about 218.5 miles apart.
Solving for the distance between the boat and the whale:Using the Pythagorean theorem to calculate the distance between the boat and the whale.
Let's call the distance between the boat and the whale "d" and the time they moved apart "t".
1st movement:
d = 45t
2nd movement:
d = (45t + 25(t+35))²
To calculate the final distance, we need to square d from the second movement and add the result from the first movement.
d² = (45t)² + (25(t+35))²
We know that the boat and the whale were moving apart for 35 minutes and 25 minutes, so we can substitute t = 35 and t = 25 in the equation.
d² = (4535)² + (2560)²
Taking the square root of the result and get the final distance between the boat and the whale.
d = ([tex]\sqrt{4535 ^{2} +2560^{2} }[/tex])
d ≈ 218.5 miles
Hence, the boat and the whale are about 218.5 miles apart.
Learn more about Distance calculations on
https://brainly.com/question/17425575
#SPJ1
Mr. Christopher contributed #500 to a business, Miss Uche contributed #300 while Mrs. Amaka contributed #200. First the share of Mr. Christopher if they share a profit #2000 according to the amount contributed.
Answers
The profit for Mr Christopher is #1000.
What is profit?Profit is the money that is earned in trade or business after paying the costs of producing and selling goods and services.
Given that, Mr. Christopher contributed #500 to a business, Miss Uche contributed #300 while Mrs. Amaka contributed #200, they share a profit #2000,
Let the ratio of their contribution = 5x : 3x : 2x
Therefore,
5x + 3x + 2x = 2000
10x = 2000
x = 200
Their profit share =
Mr. Christopher = 200 x 5 = 1000,
Miss Uche = 200 x 2 = 200
and
Mrs. Amaka = 200 x 3 = 600
Hence, the profit share of Mr. Christopher is #1000,
Learn more about profit, click;
https://brainly.com/question/23423917
#SPJ1
Which expression represents the total area of the rectangle. (look at picture)
