Answer:
The speed of the plane in still air and the speed of the jet stream are 525 miles per hour and 75 miles per hour.
Step-by-step explanation:
From Mechanical Physics, we know that absolute velocity of the airplane ([tex]v_{A}[/tex]) is equal to sum of the absolute velocity of the jet steam [tex](v_{J})[/tex] and the relative velocity of the airplane with respect to jet stream (velocity of the airplane in still air) ([tex]v_{A/J}[/tex]). Al velocities are measured in miles per hour. Let suppose that both jet stream and airplanes travels at constant velocity. Now, we construct the following system of linear equations:
Flight with the jet stream
[tex]v_{J}+v_{A/J} = \frac{2700\,mi}{4.5\,h}[/tex]
[tex]v_{J}+v_{A/J} = 600\,\frac{mi}{h}[/tex] (1)
Flight against the jet stream
[tex]v_{J} -v_{A/J} = -\frac{2700\,mi}{6\,h}[/tex]
[tex]v_{J}-v_{A/J} = -450\,\frac{mi}{h}[/tex] (2)
The solution of this system of linear equations is:
[tex]v_{J} = 75\,\frac{mi}{h}[/tex], [tex]v_{A/J} = 525\,\frac{mi}{h}[/tex]
The speed of the plane in still air and the speed of the jet stream are 525 miles per hour and 75 miles per hour.
Jack was 14 years older than Priscilla. Together their ages totaled 158 years. What were their ages?
Answer:
Jack's age: 86, Priscilla's age: 72
Step-by-step explanation:
Priscilla's age can be called x, which makes Jack's x + 14. We know that their added ages total 158 years which means that x + x + 14 = 158, which means that 2x + 14 = 158. We can then solve this by subtracting 14 on both sides and getting 2x = 144. We can divide on both sides to get that x = 72. Since Priscilla's age is x and Jack's is x + 14, we already know Priscilla's age and we need to find Jacks by adding 14 to 72. 72 + 14 = 86, so Jack's age is 86.
Answer:
Jack is 86 years old,
and Priscilla is 72 years old
Step-by-step explanation:
j = Jack
p = Priscilla
j - 14 = p $\Rightarrow$ j = p+14
j+p = 158
By subsituting the value of j ( first equation) into the second equation, we get:
p+14+p = 158
2p+14 = 158
2p = 144
p = 72.
So, j = 86
By definition, the determinant equals ad - bc. What is the value of when x = -2 and y = 3? I NEED HELP PLEASE
Answer:
B. -84Step-by-step explanation:
Taking the determinant of the matrices we will have;
= 4x(5y) - 2x(3y)
= 20xy - 6xy
= 14xy
Given x = -2 and y = 3
Determinant = 14(-2)(3)
Determinant = -28*3
Determinant = -84
What would this be??????
Answer:
I think it's the second one(200(1.034)t = 250)
Step-by-step explanation:
if not correct me. or try the third one.
On a given day, the proportion of workers from Company B who purchase a coffee from the company cafeteria is 0.62 and the proportion of workers from Company C who purchase a coffee from the company cafeteria is 0.71. A random sample of40 workers was selected from Company B and another random sample of 40 workers was selected from Company C. The proportion of workers from Company B who purchased coffee was
Answer:
the proportion of workers from company B who purchsed coffee was pˆC=0.75
Step-by-step explanation:
Answer: pˆC=0.75
Step-by-step explanation:
A jet plane can carry up to 200,000 liters of fuel. It used to 130,000 liters of fuel during a flights. What percentage of the fuel capacity did it use on this flight?
plz plz plz
i am running out the time
Answer:
mode:7
range:8
Step-by-step explanation:
mode is the most repeated number
range is the greatest -smallest number
what is 3 over 40 written as a decimal ?
Answer:
0.075
Step-by-step explanation:
3/40 = 0.075
hope it help u
plz follow me
28 decreased by 2.6%
Answer:
Please check the explanation.
Step-by-step explanation:
Given
28 decreased by 2.6%First we need to determine the percentage decrease such as:
Percentage decrease = 2.6% of 28
= 2.6/100 × 28
= 0.026 × 28
= 0.73
New value can be determined using the formula
New vaue = 28 - percentage decrease
= 28 - 0.73
= 27.27
Dawn is making an abstract painting with two triangles. the dimensions are 6 in by 10 in and 8 in by 10 in. what is the total area in square inches.
Anwser: First triangle area =0.5*8*10=40 in2. Secound triangle area =0.5*8*6=24 in2 Sum is 1st area + 2nd area, which is 64 in2.
Emmaline bought a new book for $12 with a coupon for 25% off, how much would it cost without the coupon
Answer:
$16
Step-by-step explanation:
[tex]0.75x = 12\\3x = 48\\x = 16[/tex]
Select all that are equivalent to sin H.
1. cos H
2. cos Y
3. sin Y
4. sin W
5. tan W
6. cos(90-H)
7. sin(90-H)
Answer:
i believe 1-3-5
Step-by-step explanation:
Answer: the 2nd and 6th
Step-by-step explanation:
i did the test thing
Which is the product in the expression 5(z+6)-25+x
A triangle has vertices at (-2,-3),(4, -3), and (3,5). What is the area of the triangle?
Answer:
this triangle is ABC with A(-2 ; -3), B(4; - 3) and C(3;5)
=> [tex]AB=\sqrt{(4-(-2))^{2}+\sqrt{(-3 -(-3))^{2} } }=\sqrt{6^{2} }=6\\\\AC=\sqrt{(3-(-2))^{2}+(5-(-3))^{2} }=\sqrt{5^{2}+8^{2} }=\sqrt{89}\\\\BC =\sqrt{1^{2}+8^{2} }=\sqrt{65}[/tex]
using Heron theorem, we have:
[tex]S=\sqrt{p(p-AB)(p-AC)(p-BC)}\\\\S=\sqrt{(\frac{6+\sqrt{89}+\sqrt{65} }{2})(\frac{\sqrt{89}+\sqrt{65}-6 }{2} )(\frac{6+\sqrt{65}-\sqrt{89} }{2})(\frac{6+\sqrt{89}-\sqrt{65} }{2}) }\\\\S=24 \\\\[/tex]
with S is the area of the triangle
[tex]p=\frac{AB+AC+BC}{2}=\frac{6+\sqrt{89}+\sqrt{65} }{2}[/tex]
Step-by-step explanation:
Area of the triangle with given vertices is equals to 24 square units.
What is Area?"Area is the surface which represents the total space occupied by any two dimensional object."
What is triangle?"Triangle is a polygon which has three sides and three vertices. Sum of all the interior angles of a triangle is equals to 180°."
Formula used
In ΔABC , A(x₁ , y₁) , B(x₂, y₂) and C(x₃, y₃)
Area of a triangle = [tex]\frac{1}{2} [ x_{1} (y_{2} -y_{3} + x_{2} (y_{3} -y_{1} +x_{3} (y_{1} -y_{2} ]\\[/tex]
According to the question,
Let ABC be the triangle with A(-2,-3) , B(4,-3) and C(3,5)
Area of the triangle = [tex]\frac{1}{2}[/tex] [ -2(-3-5) + 4(5+3) +3 (-3 +3)]
= [tex]\frac{1}{2}[/tex] [ 16 +32 + 0]
= 24 square units
Hence Area of the triangle with given vertices is equals to 24 square units.
Learn more about Area of the triangle here
https://brainly.com/question/19305981
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11. Twyla and Tony have a 30/5 balloon mortgage for $389,900 with a rate of 4.85%. How much will they pay in interest over the life of the loan? (3 points)
O $81,373.41
$92,263.82
O $107,536.50
O $121,390.73
Answer:
Explanation:
Twyla and Tony with a balloon mortgage of 30/5 will make constant payments over the space of 5 years and then complete the bulk balloon payment for 25 years remaining.
Given mortgage loan value of $389900
Interest rate of 4.85%
We are asked to calculate the interest over the life of the loan.
We will calculate interest by calculating constant payments over the period of 5 years before balloon payment is due and adding them together then subtracting the mortgage loan given $389900
Formula for constant payments :
A= P×r×r(1+r)^n/(1+r)^n-1
Where A= constant/monthly payments
r= interest rate on the mortgage loan
n= number of payments = 30×12= 360
P= mortgage loan given
A= $389900×0.0485×0.0485(1+0.0485)^360/(1+0.0485)^360-1
=$389900×0.0485×1231340.79/25388468.94
=$389900×0.0485×0.04850
A= $917.142
Payment for five years(with interest)= $917.142×60= $55028.52
Calculate balloon payment:
FV= PV(1+r)^n - P((1+r)^n-1/r)
Where FV= future value of balloon payment
PV= initial loan given
r= interest rate on loan
n= number of payments
P= monthly payments
Substitute:
FV= $389900(1+0.0485/12)^60-917.142((1+0.0485/12)^60-1/0.0485/12)
=$389900×1.2738-917.142(0.2738/0.004041)
=$389900×1.2738-917.142×67.756
= 496654.62-62141.87
FV = $434512.75
Therefore total payment made with interest over the life of the loan= balloon payment+ constant payments for five years= $434512.75+$55028.52
=
Evaluate:
65−15÷5 +(−19)
Answer:
43
Step-by-step explanation:
65-15/5+(-19)
65-3+(-19)
62-19=43
(a) What is wrong with the following equation? x2 + x − 42 x − 6 = x + 7 (x − 6)(x + 7) ≠ x2 + x − 42 The left-hand side is not defined for x = 0, but the right-hand side is. The left-hand side is not defined for x = 6, but the right-hand side is. None of these — the equation is correct. (b) In view of part (a), explain why the equation lim x → 6 x2 + x − 42 x − 6 = lim x → 6 (x + 7) is correct. Since x2 + x − 42 x − 6 and x + 7 are both continuous, the equation follows. Since the equation holds for all x ≠ 6, it follows that both sides of the equation approach the same limit as x → 6. This equation follows from the fact that the equation in part (a) is correct. None of these — the equation is not correct.
Answer:
Attached please find answer
Step-by-step explanation:
= (x² + x - 42) / (x - 6)
= [x² + (7x - 6x) - 42] / (x - 6)
= [x² + 7x - 6x - 42] / (x - 6)
= [(x² + 7x) - (6x + 42)] / (x - 6)
= [x(x + 7) - 6(x + 7)] / (x - 6)
= [(x + 7)(x - 6)] / (x - 6)
= x + 7 → when x approches 6
= 6 + 7
= 13
Other method:
Lim (x² + x - 42) / (x - 6)
x→ 6
When x → 6, there is an indeterminate expression because: 6 - 6 = 0
Do you know the l'Hôpital's rule, when x → a:
Lim [ f(x) / g(x) ] = Lim [ f'(x) / g'(x) ]
f(x) = x² + x - 42
f'(x) = 2x + 1
g(x) = x - 6
g'(x) = 1
= f'(x) / g'(x)
= (2x + 1)/1
= 2x + 1 → when x approches 6
= 12 + 1
= 13
What is ( 2 ⅓ * x ) + x?
Answer:
10x/3
Step-by-step explanation:
10x/3.............................
what is the equation for the line shown? picture attached.
There are 8 circles and 10 triangles. What is the simplest ratio of circles to total shapes?
The simplest ratio is 4:9
Can someone please help me Im so stressed out .
Answer:
38 students chose to fly
Step-by-step explanation:
add the female and male
If you Start with $10 in the bank and each month you add $20 which line equation will give you your total amount after X months?
Answer:
y=20x+10
Step-by-step explanation:
You start with $10, so this will be added on, and is not affected by the number of months.
You add $20 each month, so the 20 is dependant on x.
ANSWER: y=20x+10
Please help, I will give brainliest, I am struggling badly.
Answer: y = 5/2x - 4
Step-by-step explanation:
the equation is y = ax + b (a ≠ 0)
because the slope of the line is 5/2 => a = 5/2
the line passes through (0; -4) => -4 = b
=> the equation is y = 5/2.x - 4
Please help, will make brainliest
Answer/Step-by-step explanation:
1. Sin A = opp/hyp
Opp = 3
Hyp = 5
[tex] sin(A) = \frac{3}{5} [/tex] (substitution)
[tex] sin(A) = 0.6 [/tex]
2. Sin B = opp/hyp
Opp = 4
Hyp = 5
[tex] sin(B) = \frac{4}{5} [/tex] (substitution)
[tex] sin(B) = 0.8 [/tex]
3. Cos Q = adjacent/hypotenuse
Adjacent = 12
Hypotenuse = 13
[tex] cos(Q) = \frac{12}{13} [/tex] (substitution)
[tex] cos(Q) = 0.9231 [/tex] (4 decimal places)
4. Cos S = adjacent/hypotenuse
Adjacent = 5
Hypotenuse = 13
[tex] cos(S) = \frac{5}{13} [/tex] (substitution)
[tex] cos(S) = 0.3846 [/tex] (4 decimal places)
Find the percent of a number 20% of 155
Hey there!
[tex]\text{The word \underline{of} means \underline{multiply} in \underline{mathematical terms}}[/tex]
[tex]\bold{Equation: 20\% \times 155}\\\bold{20\% = \dfrac{20}{100}=\dfrac{20\div20}{100\div20}=\dfrac{1}{5}}\\\bold{\dfrac{1}{5}\times 155=?}\\\bold{155\times1=155}\\\\\bold{\dfrac{155}{5}=31}\\\boxed{\boxed{\bold{Answer: 31}}}\huge\checkmark[/tex]
Good luck on your assignment and enjoy your day!
~[tex]\frak{Amphitrite1040:)}[/tex]
Do Now
The ratio of girls to boys in a classroom is 3.1. How many boys are there in the classroom if
it has 12 girlS
Answer: 4
Step-by-step explanation:
To find out how many boys are in the classroom you must divide 12 from 3 to find the rate of change. 12/3= 4 so then you multiply 1*4 to find out how many boys are in the classroom. 1*4=4
Hope this helps ;)
Answer:
4 boys
Step-by-step explanation:
3:1 is the ratio of girls to boys
Lets girls be g and boys be b
G=3
B=1
G=12 12/3=4 and what you do to one side you do to the other it is multiplied by 4 so
B=1 time 4 =4
write 56
as the product of prime factors
[tex]56 = 28 \times 2 \\ 56 = (14 \times 2) \times 2 \\ 56 = (7 \times 2) \times 2 \times 2[/tex]
last question:) thanks guys
Answer:
5/12
Step-by-step explanation:
Probability of getting either heads or tails of a coin : 1/2
Probability of getting 1,2,3,4, or 6 on a dice: 5/6
Multiply those two probabilities : 1/2 * 5/6 = 5/12
You have a 5 out of 12 chances of getting heads on a coin AND any number but a 5 on a dice.
Hope this helps!
sarah spent a total of 10 on oranges and apples at the supet marke
t. if she spent 3 dollars less for oranges than she did on apples how much did sarah spend on oranges
A week have five school days and two weekend days. Write as ratio
Answer:
5:2
Step-by-step explanation:
2. Robert has three jobs. He worked at Young's Grocery and earned $5,805. He was a waiter at the A & B Restaurant and earned $12,445. He also earned $56,002
working for CCD Communications. Each employer took out 6.2% for Social Security. How much did Robert pay in Social Security?
Answer:
Robert paid $4,603.6 in Social Security.
Step-by-step explanation:
Robert total earnings:
$5,805 at Young's Grocery.
$12,445 at A&B Restaurant.
$56,002 at CCD Communications.
So his total earnings are of:
5805 + 12445 + 56002 = $74,252
How much did Robert pay in Social Security?
6.2%, that is, 0.062 of $74,252. So
0.062*74252 = $4,603.6
