Answer:
The coordinate of the rest stop is: [tex](5,2.5)[/tex]
The distance between the hotel and the stadium is 32 miles
Step-by-step explanation:
Given
[tex](x_1,y_1) = (3,4)[/tex] --- Team hotel
[tex](x_2,y_2) = (7,1)[/tex] --- Stadium
Solving (a): The coordinates of the rest stop
The rest stop is at half way;
So, the coordinate is:
[tex](x,y) = \frac{1}{2}(x_1+x_2,y_1+y_2)[/tex]
This gives:
[tex](x,y) = \frac{1}{2}(3+7,4+1)[/tex]
[tex](x,y) = \frac{1}{2}(10,5)[/tex]
Open bracket
[tex](x,y) = (5,2.5)[/tex]
Solving (b): Distance between the hotel and the stadium
We have:
[tex](x_1,y_1) = (3,4)[/tex] --- Team hotel
[tex](x_2,y_2) = (7,1)[/tex] --- Stadium
The distance (d) is:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]d = \sqrt{(3 - 7)^2 + (4 - 1)^2}[/tex]
[tex]d = \sqrt{(-4)^2 + 3^2}[/tex]
[tex]d = \sqrt{16 + 9}[/tex]
[tex]d = \sqrt{25}[/tex]
[tex]d =5[/tex]
From the question, we have:
[tex]1\ unit = 6.4\ miles[/tex]
So:
[tex]d =5 * 6.4\ miles[/tex]
[tex]d =32\ miles[/tex]
Find the value of the trig function indicated.
Answer:
[tex]\displaystyle cos\theta = \frac{2\sqrt{13}}{13}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTrigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is a legb is another legc is the hypotenuse[Right Triangles Only] SOHCAHTOA
[Right Triangles Only] cosθ = adjacent over hypotenuse
Step-by-step explanation:
Step 1: Define
Identify variables
a = 8
b = 12
c
Step 2: Solve for c
Substitute in variables [Pythagorean Theorem]: 8² + 12² = c²Evaluate exponents: 64 + 144 = c²Add: 208 = c²[Equality Property] Square root both sides: √208 = cRewrite: c = √208Simplify: c = 4√13Step 3: Define Pt. 2
Identify variables
Angle θ
Adjacent leg = 8
Hypotenuse = 4√13
Step 4: Find
Substitute in variables [Cosine]: [tex]\displaystyle cos\theta = \frac{8}{4\sqrt{13}}[/tex]Rationalize: [tex]\displaystyle cos\theta = \frac{2\sqrt{13}}{13}[/tex]Answer:
Solution given;
In right angled triangle with respect to θ
perpendicular: opposite side: [P]=12
base:adjacent:[b]=8
hypotenuse [h]=?
cosθ=?
According to the Pythagoras law
h²=p²+b²
h²=12²+8²
h=[tex] \sqrt{208}[/tex]
h=[tex] 4\sqrt{13}[/tex]
Now
we have
Cos θ=[tex]\frac{adjacent}{hypotenuse}[/tex]
Cos θ=[tex]\frac{8}{4\sqrt{13}}[/tex]
by rationalising it
Cos θ= [tex] \frac{2\sqrt{13}}{\sqrt{13}×\sqrt{13}}[/tex]
Cos θ= [tex] \frac{2\sqrt{13}}{13}[/tex]
is a required answer.
You want to make five-letter codes that use the letters A, F, E, R, and without repeating any letter. What is the probability that a randomly chosen
code starts with Mand ends with E?
Answer:
Probability [chosen code starts with M and ends with E] = 0.05
Step-by-step explanation:
Given:
Total alphabet = A, F, E, R, and M
Creating name without repeat
Find:
Probability [chosen code starts with M and ends with E]
Computation:
Probability Name start with M = 1 / 5
Probability Name start with E = 1 / (5-1)
Probability Name start with E = 1 / 4
Probability [chosen code starts with M and ends with E] = Probability Name start with M x Probability Name start with E
Probability [chosen code starts with M and ends with E] = (1/5)(1/4)
Probability [chosen code starts with M and ends with E] = 1 / 20
Probability [chosen code starts with M and ends with E] = 0.05
(x-4) (2x+5)(x+7) (x+7)(3x-4)(2x-5)
simplify it pls
Answer: 12x^6+104x^5-319x^4-2890x^3+4661x^2+14000x-19600 sorry I don't have enough time to explain I got to go hope that helps tell me if I was right or not bye!
Step-by-step explanation:
3. Three resistors with values of 3 Ω, 4 Ω and 5 Ω are connected to a 12 V battery.
a. Draw the circuit.
b. Calculate the equivalent resistance of the circuit.
c. Calculate the current through the battery.
d. How much current is passing through each resistor?
e. Calculate the voltage drop across each resistor.
f. How does the voltage drop across each resistor compare to the voltage of the battery?
4. Three resistors with values of 12 Ω, 24 Ω and 6 Ω are connected in series to one another and a 24 V power supply. Draw the circuit and fill in the data table.
Answer:
I think it's 4
Step-by-step explanation:
Three resistors with values of 12 Ω, 24 Ω and 6 Ω are connected in series to one another and a 24 V power supply. Draw the circuit and fill in the data table.
What is the area of the shape?
Answer:
20 is the answer :))))
20
the diameter of a circle is 24 meters what is the circumference
Answer:
The circumfrence is 75.36
Step-by-step explanation:
I hope this helps
Find the area of the shape
Pleaseeee helpppp meeee nowwwww
Answer:
The rate of change would be $3.50 per gallon.
Step-by-step explanation:
In the graph depicted in the picture, when the number of gallons increases by 2, the price increases by $7. Since the graph maintains a constant rate of change, that means the rate of change would be [tex]\frac{7}{2}[/tex] or $3.50 per gallon.
Hayden wants to find out what grade he must receive on his next math test in order to receive a 90 on his report card. His current math test grades are a 90, 89, 91, and 92. Which measure of center would be best for him to use
Answer: Mean
Step-by-step explanation:
Mean is best used when the numbers in the data set are close together and the number of outliers are limited because outliers will either increase or decrease the mean such that it would not be a true representation of the data set.
In cases like the above however where the numbers are generally in the same range, the mean would provide a center measure that is the most representative because it would simply be a simple average of the numbers.
PLEASE!!! I JUST REALLY NEED HELP RIGHT NOW! T∆T
Using the 45o -45o -90o triangle theorem, solve this triangle.
Answer:
Step-by-step explanation:
take 45 degree as reference angle
using sin rule
sin 45 =opposite /hypotenuse
1/[tex]\sqrt{2}[/tex]=24/k(do cross multiplication)
24[tex]\sqrt{2}[/tex]=k
If you doubled joes age and added 10 years he would still be younger than his uncle. His uncle is 51. Use inequalities to find how old Joe is.
Answer:
He is 20 at oldest, or [tex]x\leq 20[/tex]
Step-by-step explanation:
The first step in finding a possible age is:
Subtract 10 from 51, and you get 41. Divide by 2, and you get about 20.5.
This means Joe is younger than or 20 years old.
which numbers chart follows the rule add 7
Jack bought 50 lbs of clay for his art projects. He used 13.2 lbs to make a sculpture, and 0.72 lbs for each mug. How many mugs did Jack make if he had 28.88 lbs of clay left over?
Please help me I really need the answer I have to do 6 more assignments and Helping me would really help me finishing.
Given :
Jack bought 50 lbs of clay for his art projects. He used 13.2 lbs to make a sculpture, and 0.72 lbs for each mug.
To Find :
How many mugs did Jack make if he had 28.88 lbs of clay left over.
Solution :
Clay required to make 1 mug, r = 0.72 lbs.
Amount of clay left after making sculpture is, T = 28.88 lbs.
Now, number of clay mug Jack can make is :
[tex]n = \dfrac{28.88}{0.72}\\\\n= 40.11[/tex]
Since, number of mug cannot be in decimal, so we take the floor value.
Therefore, number of mug that can be prepared is 40 .
The second item for a restaurant is a circular pancake. They make 6 inch diameter
pancakes and charge $1.50 per pancake. They want to make 8 inch diameter
pancakes, how much should they charge for this larger pancake?
need help quickly please!
Answer:
86
Step-by-step explanation:
Considering that it is a triangle ABC which means AB = AC + BC AB = 48 + 38 = 86
I think that's it I hope it will help you
Which of the following best describes the shape of the distribution below ?
A) Uniform
B) right skewed
C) bell shaped
D) left skewed
Answer:
Its right skewed
find the measurement of DAE
Can you please give attachments? Thank you :)
This Stem-and-Leaf Plot shows the number of people who attended a local nine-day carnival.
Which statement is not true about this data set?
A. The range is 50 people.
B. The median is 65 people.
C. The mean is 65 people.
D. The mode is 65 people.
Answer:
C) this is the false statement
Step-by-step explanation:
data set in list form:
35, 42, 45, 55, 65, 65, 68, 76, 85
Range: 85-35 = 50
Median: 65
Mean: 536/9 = 59.5
Mode: 65
The statement that is not true about this data set is C. The mean is 65 people.
This Stem-and-Leaf Plot shows the number of people who attended a local nine-day carnival.
The data set in list form:
35, 42, 45, 55, 65, 65, 68, 76, 85
How to find the mean and median of a data?Mean is the ratio of sum of the observations to the total number of observations.
Mean: 536/9 = 59.5
Median is such a number for the arranged data set(ascending or descending order) such that to its left and to its right belong same number of observations.
Median: 65
Range = Maximum value of the data set - Minimum value of the dataset
Range: 85-35 = 50
Mode is the number in given data that occurs frequently.
Mode: 65
Learn more about skewed distribution here:
https://brainly.com/question/13111221
#SPJ2
A spherical dodge ball has a radius r and a tennis ball has a radius 0.3r? What is the difference in volume between a dodge ball and a tennis ball?
Answer:
4/3π(0.973r³)
Step-by-step explanation:
Volume of a sphere = 4/3πr³
Given the radius of dodge ball rd = r
radius of tennis ball rt = 0.3r
Taking their difference
Volume difference = 4/3πrd³ - 4/3πrt³
Volume difference = 4/3π(r)³ - 4/3π(0.3r)³
Volume difference = 4/3π(r³ - 0.027r³)
Volume difference = 4/3π(0.973r³)
Hence the differmce in volume is 4/3π(0.973r³)
Given the system of linear equations:
4x + 6y = 24
2x+y=8.
Which equations (select all) are a result from ADDING and/or SUBTRACTING the TWO
equations together?
6x + 7y = 32
2x + 6y = 16
2x + 5y = 16
63 - 6y = 32
Which graph below shows a line that contains ordered pairs that are solutions of the equation shown?
y = –x + 4
Given:
The equation is:
[tex]y=-x+4[/tex]
To find:
The graph of the line that contains ordered pairs that are solutions of the given equation.
Solution:
We need to find the graph of the given equation.
We have,
[tex]y=-x+4[/tex]
At [tex]x=0[/tex], we get
[tex]y=-0+4[/tex]
[tex]y=4[/tex]
So, the x-intercept of the given equation is at point (0,4).
At [tex]y=0[/tex], we get
[tex]0=-x+4[/tex]
[tex]x=4[/tex]
So, the y-intercept of the given equation is at point (4,0).
From the given graphs it is clear that the line in option C has x-intercept at point (0,4) and y-intercept at point (4,0).
Therefore, the correct option is C.
The tree diagram shows Leila's choices for dinner at a restaurant. How many possible dinner combinations exist?
Based on the tree diagram, there are a total of 12 possible dinner combinations for Leila.
Define combinations?
In mathematics, combinations are a way to count the number of ways to choose a subset of items from a larger set, where the order of the chosen items does not matter. The number of combinations is often denoted using the symbol "n choose k", where n is the total number of items and k is the number of items being chosen.
To see why, we can count the number of paths through the tree diagram. Starting at the top, there are 2 choices for the type of dips: Guacamole dip or Cheese dip. For each of these choices, there are 2 choices for the dessert : Burrito and Enchilada. Finally, for each main course, there are 2 choices for the main course: Chicken and Beef.
Multiplying the number of choices at each step, we get:
2 (choices for dips) x 2 (choices for dessert) x 2 (choices for main course) = 8 possible dinner combinations.
Therefore, there are 3 possible dinner combinations for Leila.
To learn more about subset from the given link :
https://brainly.com/question/23454979
#SPJ1
hey! i’ll give brainliest pls help.
Answer:
C) The fossil is between 10 million and 50 million years old.
Step-by-step explanation:
Since Layer B is located between Layer A and C, option C is the only reasonable answer because Layer A is 50 million years old and Layer C is 10 million years old.
do you know how to solve this?
Answer:
a) 36yards
Step-by-step explanation:
I just took the test
Help please like this is due in 30 minutes if you don’t know don’t answer
Answer:
Step-by-step explanation:
6 no answer 0,9
7 no answer -3,-10
8 no answer -10,2
9 no answer 2,0
hope this helps u!!
what will the remainder over the divisor?
Which set of shapes could be used to form a net for a square pyramid?
1 square and 4 triangles
2 squares and 4 triangles
1 square and 4 rectangles
2 squares and 4 rectangles
Answer:
1 square and 4 triangles
Step-by-step explanation:
Answer:
The answer is (A) or 1 square and 4 triangles .
Step-by-step explanation:
Looking at a picture of a square pyramid would help to answer this question. (Btw sorry if im late) Stay safe<3 .
Please give me answer find the odd option
Answer:
should be the third (81,90)
Step-by-step explanation:
Which choice is equivalent to the expression below?
√20 + √45
→ √20 + √45
→ 2√5 + 3√5
Taking √5 as common.→ (2 + 3)√5
→ 5√5
Therefore, option A is correct.
which one is it?‼️‼️
Answer:
C
Step-by-step explanation:
20 ÷ 5 = 4
24 ÷ 6 = 4
28 ÷ 7 = 4
32 ÷ 8 = 4
So the correct answer is C