The plane travels at 60 mph and the wind is blowing at 20 mph.
By setting up and solving a system of equations, we find that the speed of the plane in still air is 63 mph and the speed of the wind is 21 mph.
Explanation:To answer this question, you first need to set up equations to represent the speed of the plane and the speed of the wind. You can denote the speed of the plane in still air as 'p' and the speed of the wind as 'w'. The plane's speed with the wind (going to Phoenix) is represented by p+w and against the wind (coming back) is p-w.
For the trip to Phoenix, you know that distance = speed * time. That gives us the equation 1176 = 14(p+w). After simplification, we obtain the equation, p+w = 84.
For the return flight, our equation is 1176 = 28(p-w). On simplification, we find the equation p-w = 42.
Now you have a system of equations that you can solve: p+w = 84p-w = 42. Solving these equations together, you find that the speed of the plane (p) in still air is 63 mph, and the speed of the wind (w) is 21 mph.
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Mr.Walden wrote the expression p^-5/q^0. He asked his students to write an equivalent expression of p^-5/q^0 simplified form. Four students wrote these expressions. Isaac q^0/p^-5 Rosa p^-5+p^0 Bruce p^5q^0 Brianna 1/p^5q^0 Which student is correct? Isaac Rosa Bruce Brianna
The correct option is Brianna's equation [tex]\dfrac{1}{p^5q^0}[/tex].
To find the correct simplification of given expression we have to apply negative exponent rule.
Given:
The given expression is [tex]\dfrac{p^{-5}}{q^0}[/tex].
What is negative exponent rule?The negative exponent can be change in to positive by writing same in denominator and 1 in numerator.
Simplify the given expression.
[tex]\dfrac{p^{-5}}{q^0}=\dfrac{1}{p^5q^0}[/tex]
Thus, the correct option is Brianna's equation [tex]\dfrac{1}{p^5q^0}[/tex].
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In a basketball tournament, Team A scored 5 fewer than twice as many points as Team B. Team C scored 80 more points than Team B. The combined score for all three teams was 983 points. Write an equation to represent this scenario using the variable b to represent Team B’s total points.
Answer:
Team A= 2b-5
Team B= b
Team C= b+80
The equation representing this scenario is (2b-5)+ b + (b+80)= 983
Step-by-step explanation:
Solving the equation b + (2b - 5) + (b + 80) = 983, we found that Team B scored 227 points. Therefore, Team A scored 449 points and Team C scored 307 points.
To represent the scenario mathematically, let's define the variable b as the total points scored by Team B. Then, we can express the points scored by the other two teams in terms of b:
Team A scored 5 fewer than twice as many points as Team B: 2b - 5Team C scored 80 more points than Team B: b + 80The combined score for all three teams was 983 points. Thus, we can write the equation:
b + (2b - 5) + (b + 80) = 983.Simplify the equation step-by-step:
Combine like terms: 4b + 75 = 983Subtract 75 from both sides: 4b = 908Divide by 4: b = 227So, Team B scored 227 points.
How do you multiply 3/10x8/9=
Hello!
[tex]\frac{3}{10}*\frac{8}{9}[/tex]
Explanation:
↓↓↓↓↓↓↓↓↓↓
First you had to multiply by the fractions.
[tex]\frac{3*8}{10*9}[/tex]
Then you can multiply by the numbers.
[tex]\frac{24}{10*9}[/tex]
Next you can also multiply by the numbers again.
[tex]\frac{24}{90}[/tex]
You can also can the common factor of 6.
[tex]\frac{4}{15}[/tex]
Answer⇒⇒⇒⇒⇒4/15
Hope this helps!
Thank you for posting your question at here on Brainly.
Have a great day!
-Charlie
what is the simplest form of 0.875 as a fraction
If f(x) = 10 + 50x, solve for x when f(x) = 310.
x = 6
given f(x) = 310, we obtain the equation
10 + 50x = 310 ( subtract 10 from both sides )
50x = 300 ( divide both sides by 50 )
x = [tex]\frac{300}{50}[/tex] = 6
Can someone please give me the answer to these questions ?
Not for just 5 points...
1.There are 167960 different ways the list of starting players could be formed.
2. The number of ways to write the batting order is 362880.
3. 42,758,676 different ways the group of interviewees can be made.
4. The total number of ways the students can win first, second, or third place is 144 ways.
5. The total number of different answer keys possible is 4096 ways.
1. **Varsity Baseball Team:**
There are 20 students on the team, and 9 will be chosen for the starting lineup. The number of ways to choose 9 out of 20 students is calculated by the binomial coefficient formula, also known as "20 choose 9":
[tex]\[ \binom{20}{9} = \frac{20!}{9!(20-9)!} = 167960. \][/tex]
2. **Batting Order:**
Once the starting lineup is selected, there are 9 players. The first position can be any of the 9 players, the second position can be any of the remaining 8 players, and so on. So, the number of ways to write the batting order is [tex]\(9! = 362880\) (9 factorial).[/tex]
3. **Jury Duty:**
There are 42 citizens, and 11 need to be chosen. The number of ways to choose 11 out of 42 is given by the binomial coefficient [tex]\(\binom{42}{11} = \frac{42!}{11!(42-11)!}\).[/tex] Calculating this gives [tex]\(42,758,676\)[/tex] different ways the group of interviewees can be made.
4. **Spelling Bee:**
There are 24 students competing for first, second, and third place. For the first place, there are 24 choices, for the second place, there are 23 choices (as one student has already won the first place), and for the third place, there are 22 choices left. So, the total number of ways the students can win first, second, or third place is [tex]\(24 \times 23 \times 22 = 12,144\)[/tex] ways.
5. **Multiple Choice Test:**
Each of the 6 questions has 4 possible answers. For each question, there are 4 choices. Since there are 6 questions, the total number of different answer keys possible is [tex]\(4^6 = 4096\)[/tex] ways.
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Brainliest + points! Help please! Mathematicians
Answer and explain (No its not the lower extreme etc. Its the values and the actual numbers)
There are 5 parts of a box-and-whisker plot.
Lowest Value (Minimum)= that's the left end of the graph, and shows what the minimum value is. Here, the minimum is 46.
Lower Quartile (Q₁)= This is the left edge of the "box" in a box-and-whisker plot. Here it is 55.
Median (Q₂)= This is the line in the middle of the box, and represents the very center of minimum and maximum values. Here it is 58.
Upper Quartile (Q₃)= This is the right edge of the box in a box-and-whisker plot. Here it is 63.
Highest Value (Maximum)= This is the farthest right point on your plot. Here it is 66.
Hope this helps! If you have any questions, please feel free to ask in the comments below!
The term 'lower extremes' in mathematics typically refers to the minimum value of a data set, but in this case, the student is asking for the values that represent the lower extremes.
Explanation:In mathematics, the term 'lower extremes' usually refers to the lower limit of a data set, also known as the minimum value. However, since the question specifically asks for 'values and actual numbers', we can assume that the student is referring to the values that represent the lower extremes in the data set. For example, if the data set is {3, 5, 1, 2, 7}, the lower extremes would be the values 1 and 2.
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$2.70. Calculate the cost of a movie ticket in 1995, using the Consumer Price Index of 82.4 in 1980 and 152.4 in 1995
If it's $2.70 now, the cost would be $4.45 in 1995.
To find the 1995 cost of a movie ticket that was $2.70 in 1980, divide the 1995 CPI by the 1980 CPI and multiply by the 1980 price. The calculation yields a cost of approximately $4.99 for a movie ticket in 1995.
Explanation:To calculate the cost of a movie ticket in 1995 using the Consumer Price Index (CPI) from 1980 to 1995, we can use the formula to adjust prices based on inflation:
Determine the ratio of the CPI in 1995 to the CPI in 1980.Apply this ratio to the cost of the item in 1980 to find the equivalent cost in 1995.Let's assume the cost of a movie ticket in 1980 was $2.70. The CPI for 1980 is 82.4, and for 1995 it is 152.4. We calculate the ratio as 152.4 / 82.4 = 1.8495.
Multiplying the 1980 ticket price by this ratio gives us:
$2.70 * 1.8495 = $4.99 approximately.
Therefore, the cost of a movie ticket in 1995, adjusted for inflation, would be about $4.99.
evaluate 9- 8/s when s=4
Answer:
Your answer would be 7.
Step-by-step explanation:
9 - 8/s first you divide 8 and s which in this case is 4.
8/4 is 2.
9 - 2 = 7
Therefore, your answer is 7
The required value of 9 -8/s when x = 4 is 7.
Given that,
to determine the value of the expression 9- 8/s when s=4.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
What is simplification?
The procedure in mathematics to perform and solve the expression to make expression simple or more understandable called simplify and the process is called simplification.
Here,
Let the given expression is equal to x
x = 9 - 8/s
here, s = 4
x = 9 - 8 /4
x = 9 - 2
x = 7
Thus, the required value of 9 -8/s when x = 4 is 7.
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Jackson drinks 0.44 liters of water, which was 55% of the water in the bottle. How much water was in the bottle to start?
Answer:
He had 0.8 liters to start with...
Step-by-step explanation:
0.44 is 55% of what? (what = x)
Equation: Y = P% * X
X = Y/P%
X = 0.44/55%
55% = 0.55
X = 0.44/0.55
X = 0.8
Answer:
ans is 0.8 liters
Step-by-step explanation:
Jackson drinks 0.44 liters of water, which was 55% of the water in the bottle.
Let X be the volume of water in the bottle to start.
55% of X = 0.44L
X = 0.44/55% = 0.44/55*100=44/55=4/5=0.8 liters
What happens to ice as it melts
Ice will turn to water. When ice is frozen, the particles are compact and slow. Once the ice heats up, the particles will become less compact and move faster.
0.2= what doe it equal
It equals 20%. Or 2/10
1/5 because it equal 20 percentile.
c - 1.5+6.8=0.6 what is x
Ok! I gotcha!
C-1.5+6.8=0.6
Steps:
Add/Subtract The #!
c+5.3=0.6
Subtract 5.3 On Both Sides!
c+5.3-5.3=0.6-5.3
Simplify!
c=-4.7
Which points are on the graph of the function rule ƒ(x) = 10 – 4x? ( –18, 2), ( –10, 0), ( –2, –2) (18, –2), (10, 0), (2, 2) (–2, 18), (0, 10), (2, 2) (2, –18), (0, –10), ( –2, –2)
(2, 2 ), (- 2, 18 ), (0, 10 )
substitute the x-coordinate of each point into f(x) and if the value is equal to the y-coordinate then it is on the graph of f(x)
(- 18, 2 ) ⇒ y = 10 + 72= 82 ≠ 2
(- 10, 0 ) ⇔ y = 10 + 40 = 50 ≠ 0
(- 2, - 2 )⇒ y = 10 + 8 = 18 ≠ 2
(18, - 2 ) ⇒ y = 10 - 72 = - 62 ≠ - 2
(2, 2 ) ⇒ y = 10 - 8 = 2 ⇒ (2, 2 ) is on graph
(- 2, 18 ) ⇒ y = 10 + 8 = 18 ⇒ (- 2, 18 ) is on graph
(0, 10 )⇒ y = 10 - 0 = 10 ⇒ (0, 10 ) is on graph
(2, - 18 ) ⇒ y = 10 - 8 ≠ - 18
5q greater than or equal to 8q -3/2
5q ≥ 8q - 3/2
Add 3/2 to both sides.
3/2 + 5q ≥ 8q
Subtract 5q from both sides.
3/2 ≥ 3q
Multiply both sides by 2.
3 ≥ 6q
Divide both sides by 6.
0.5 ≥ q.
The value of q is less than or equal to 0.5.
Put the following in slope intercept form
4x - 3y = 15
slope intercept form: y = mx + b
Note the equal sign. what you do to one side, you do to the other. First, subtract 4x from both sides
4x - 3y = 15
4x (-4x) - 3y = 15 (-4x)
-3y = -4x + 15
Next, divide -3 from both sides to isolate the y.
(-3y)/-3 = (-4x + 15)/-3
y = (4/3)x - 5
y = (4/3)x - 5 is your answer
hope this helps
4: Find the equation of the line perpendicular to y = ¼ x + 2, passing through the point (-3,0).
A. Y = ¼ x + ¾
B. Y = 4x + 12
C. Y = -4x – 12
D. Y = -4x + 12
Your answer is C. Y= -4x-12
jacklyn's employer matches 30% of Jacklyn's contributions to her 401(k) plan if her employer contributed $300 to the plan last year, how much did Jacklyn contribute to the plan last year?
A) $1300
B) $1000
C) $700
D) $900
B because 30% of 1000 is 300
Answer:
Option B) $1000 would be correct.
Step-by-step explanation:
Jacklyn's employer matches 30% of Jacklyn's contributions to her 401(k) plan.
Let Jacklyn's contribution = x
Her employer's contribution = 30% of x = 300
= [tex]\frac{30x}{100}[/tex] = 300
= 30x = 300 × 100
= x = 30000 ÷ 30 = $1000
Jacklyn contributed $1000 to the 401(k) plan last year.
State of the number 49/9 (square root) is a rational or irrational
A. Rational
B. Irrational
Identifying the strengths of a hero shows which character trait?
Question 1 options:
Leadership
Courage
Gratitude
Courage.
Heros often take risks, you must have courage to take risks.
Answer:
Courage
Step-by-step explanation:
Hero has some special characteristics which makes him hero
one of those characteristics of a hero is that a hero always shows courage and never fall down or run out from the situations instead he faces all the challenges with courage and never pocks down even in tricky situations.
a hero is that which helps the other when they need him in any situation or at any mode of life.a real hero does not care for his life .To save others he put his life in danger and shows courage.
all these qualities make a person a real hero.
HOW WOULD YOU DO THIS???
Write the equation of the line perpendicular to the line y = -5/7x + 12/7 and containing the point (5,2). Write your answer in slope-intercept form.
Answer:
y = 7x/5 - 5
Step-by-step explanation:
m = 7/5
y - 2 = 7/5(x - 5)
y - 2 = 7x/5 - 7
y = 7x/5 - 5
Six times a number is greater than 20 more than that number what are the possible values of that number
Let n = the unknown number.
Six times a number = 6 * n = 6n
20 more than number = n + 20
Greater than = >
Put it all together:
6n > n + 20
Subtract n from both sides to get constants on one side and variables on the other:
6n - n > 20
5n > 20
Divide both sides by 5 to isolate variable N
n > 4
or (4, ∞)
What is the solution to this equation? x + 13 = 34
Answer:
x=21
Step-by-step explanation:
Hello
The solution to the equation is the numerical values of the letters for which equality is true.
To find the value of x , you have to isolate x. to do this, you pass the 13 that is positive number to the other side of the equation,When you pass a positive number to the other side of the equation it passes as negative number.
x+13=34
x=34-13
x=21
Have a great day
there are 4 planets. the first planet has an orbit of 3 years. The second planet has an orbit of 5 years. The third planet has an orbit of 8 years. The fourth planet has an orbit of 12 years. if there in conjunction how long till they're in conjunction again? math problem answer
Find the LCM of the four numbers (3, 5, 8, 12)
3: 3
5: 5
8: 2 * 2 * 2
12: 2 * 2 * 3
LCM = 2 * 2 * 2 * 3 * 5
= 120
Answer: 120 years
Final answer:
The planets will be in conjunction again after 15 years.
Explanation:
To determine when the planets will be in conjunction again, we need to find the least common multiple (LCM) of their orbital periods.
The orbital periods of the four planets are: 3 years, 5 years, 8 years, and 12 years.
To find the LCM, we can list the multiples of each of the numbers and identify the smallest number that appears in each list.
The multiples of 3 are: 3, 6, 9, 12, 15, ...
The multiples of 5 are: 5, 10, 15, 20, 25, ...
The multiples of 8 are: 8, 16, 24, 32, ...
The multiples of 12 are: 12, 24, 36, ...
The smallest number that appears in all lists is 15, so the planets will be in conjunction again after 15 years.
Which number is a solution of the inequality? 5(2q – 8) ≥ 7 A. 6 B. –2 C. −12 D. 92
[tex]5(2q-8)\geq7\\10q-40\geq7\\10q\geq47\\q\geq4.7[/tex]
so the solution is not really a single number but a range, depending on how q is defined. I am assuming q is defined in domain of Real numbers, and then the solution to the inequality will be "all real numbers larger or equal to 4.7"
You have a shelf that holds 25 1/2 pounds. How many 1 1/4 pound books can the shelf hold? Explain your response
Answer:
20 2/5
Step-by-step explanation:
25 1/2
1 1/4
1 1/4 times 4 is 5
5 times 5 is 25
D(1) = 13 d(n) = d(n-1) + 17 find the 4th term
d(4) = 64
substitute n = 2, 3, 4 into d(n) = d(n - 1) + 17
d(2) = d(1) + 17 = 13 + 17 = 30
d(3) = d(2) + 17 = 30 + 17 = 47
d(4) = d(3) + 17 = 47 + 17 = 64
The area of a rectangle is 45 ft2. If the length of the long side of the rectangle is 80% greater than the short side of the rectangle, what is the length of the longer side?
To solve this problem we propose the following equation:
1) [tex]b*h =45\\[/tex] This is the equation of the area of a rectangle.
Where a and b are the sides of the rectangle
If b is the longest side, then
b is 80% longer than h.
2) [tex]b= h+0.8h\\[/tex]
Now we have 2 equations and two unknowns.
Therefore we solve the following equations
[tex]45=b*\frac{b}{1+0.8}\\[/tex]
[tex]b^2=45(1+0.8)[/tex]
[tex]b =\sqrt{45(1+0.8)}\\[/tex]
b = 9 feet
The length of the longest side is 9 feet.
The area of a rectangle is 45 ft^2
If the length of the long side of the rectangle is 80% greater than the short side of the rectangle.
Let the shortest side be the width (x)
Length of rectangle L = 80% greater than x
So length = 0.8 x + x
Length = 1.8 x
Area of the rectangle = Length * width
45 = 1.8x * x
[tex]45= 1.8x^2[/tex]
Divide by 1.8 from both sides'
[tex]25= x^2[/tex]
Take square root on both sides
x=5
so width of the rectangle = 5 feet
Length of the rectangle (longer side) = 1.8x = 1.8 * 5 = 9 feet
the city council wants the location of the entrance to a new city park to be determined by the reflection of the school entrance across the y-axis what are the coordinates of the entrance to the new city park on this map your answer should be (_,_) formed like that *this is 6th grade math btw* so don't think to far
The coordinates of the entrance to the new city park on this map should be (-5, -3).
What is a reflection over the y-axis?In Mathematics and Geometry, a reflection over or across the y-axis or the line y = 0 is represented by this transformation rule .
This ultimately implies that, a reflection over or across the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
By applying a reflection over the y-axis to the coordinates of the point for the school entrance (5, -3), we have the following coordinates of its image;
(x, y) → (-x, y)
(5, -3) → (-5, -3)
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