Answer:
Her velocity is 95 km/hour
Step-by-step explanation:
The given information includes;
The direction to which Anna was driving = Eastward
Her initial location on the journey = 570 kilometres west of her her exit
The distance she drove in 2 hours = 1/3 of the way to her exit
Therefore, the distance she drove in 2 hours = 1/3×570 = 190 m
Her velocity = Her distance covered/(The time it take to cover the distance)
Which gives;
Her velocity = (190 km)/(2 hours) = 95 km/hour
Her velocity = 95 km/hour.
How to work out the mean
Answer:
mean is average
1. Add all the values to find the total
2. Divide the total you have found by the amount of numbers you have added to find the total
Answer:
To work out the mean you have to add all of the numbers up then divide it by how many numbers the are
Step-by-step explanation:
help me with these please
Step-by-step explanation:
(1) y = x e^(x²)
Take derivative with respect to x:
dy/dx = x (e^(x²) 2x) + e^(x²)
dy/dx = 2x² e^(x²) + e^(x²)
dy/dx = (2x² + 1) e^(x²)
Take derivative with respect to x again:
d²y/dx² = (2x² + 1) (e^(x²) 2x) + (4x) e^(x²)
d²y/dx² = (4x³ + 2x) e^(x²) + 4x e^(x²)
d²y/dx² = (4x³ + 6x) e^(x²)
Substitute:
d²y/dx² − 2x dy/dx − 4y
= (4x³ + 6x) e^(x²) − 2x (2x² + 1) e^(x²) − 4x e^(x²)
= 4x³ + 6x − 2x (2x² + 1) − 4x
= 4x³ + 6x − 4x³ − 2x − 4x
= 0
(2) y = sin⁻¹(√x)
sin y = √x
sin²y = x
Take derivative with respect to x:
2 sin y cos y dy/dx = 1
sin(2y) dy/dx = 1
dy/dx = csc(2y)
Take derivative with respect to x again:
d²y/dx² = -csc(2y) cot(2y) 2 dy/dx
d²y/dx² = -2 csc²(2y) cot(2y)
Substitute:
2x (1 − x) d²y/dx² + (1 − 2x) dy/dx
= 2 sin²y (1 − sin²y) (-2 csc²(2y) cot(2y)) + (1 − 2 sin²y) csc(2y)
Use power reduction formula:
= (1 − cos(2y)) (1 − ½ (1 − cos(2y))) (-2 csc²(2y) cot(2y)) + (1 − (1 − cos(2y))) csc(2y)
= (1 − cos(2y)) (1 − ½ + ½ cos(2y)) (-2 csc²(2y) cot(2y)) + cos(2y) csc(2y)
= (1 − cos(2y)) (½ + ½ cos(2y)) (-2 csc²(2y) cot(2y)) + cot(2y)
= (cos(2y) − 1) (1 + cos(2y)) csc²(2y) cot(2y) + cot(2y)
= (cos²(2y) − 1) csc²(2y) cot(2y) + cot(2y)
= -sin²(2y) csc²(2y) cot(2y) + cot(2y)
= -cot(2y) + cot(2y)
= 0
area of a triangle two sides of which are 18 cm and 12 cm
and the perimeter is 44 cm.
Answer:
≈ 83.9 cm²
Step-by-step explanation:
Given:
P = a+b+c = 44 cma = 18 cmb = 12 cmThen:
c= P -(a+b) = 44 -(18+12) = 14 cmArea of the triangle is found by using Herons formula:
A = √s(s-a)(s-b)(s-c),where s = P/2 = 44/2 = 22 cm
A = √22(22-18)(22-12)(22-14) = √22*4*10*8= √7040 ≈ 83.9 cm²Answer:
[tex]\huge \boxed{\mathrm{83.9 \ cm^2}}[/tex]
Step-by-step explanation:
Two sides of the triangle are given.
The perimeter is given.
We need to solve for the third side.
[tex]P=a+b+c[/tex]
[tex]P= \sf perimeter[/tex]
[tex]a,b,c= \sf side \ lengths[/tex]
[tex]44=18+12+c[/tex]
[tex]c=14[/tex]
The measure of the third side is 14 cm.
When three sides of the triangle are given, we can solve for the area using Heron’s formula.
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]s=\sf semi \ perimeter[/tex]
[tex]\displaystyle s=\frac{P}{2} =\frac{44}{2} =22[/tex]
Plugging in the values and evaluating.
[tex]A=\sqrt{22(22-18)(22-12)(22-14)}[/tex]
[tex]A = 83.904708...[/tex]
The area of the triangle is approximately 83.9 cm².
Homer Simpson entered a pie eating contest at the county fair. Homer was determined to win and went into training for 6 days. Each
day, he ate 4 more pies than the day before. Homer ate 150 pies while in training. How many pies did he eat each day?
Day 1: type your answer...
Day 2: type your answer....
Day 4: type your answer....
Day 3: type your answer....
type your answer...
Day 5: type your answer...
Day 6: type your answer...
Answer:
151923273135Step-by-step explanation:
He ate 15, 19, 23, 27, 31, 35 pies for each day.
What is addition?Addition in math is a process of combining two or more numbers.
Given that, Homer Simpson entered a pie eating contest at the county fair. Homer was determined to win and went into training for 6 days, each day, he ate 4 more pies than the day before. Homer ate 150 pies while in training.
Let he ate x pie for 1st day, then according to question,
1st day = x
2nd day = x+4
3rd day = x+8
4th day = x+12
5th day = x+16
6th day = x+20
He ate 150 pies for 6 days
Therefore, x+x+4+x+8+x+12+x+16+x+20 = 6x + 60 = 150
6x = 90
x = 15
Hence, he ate 15, 19, 23, 27, 31, 35 pies for each consecutive day.
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Which describes the standard deviation?
Step-by-step explanation:
standard deviation is used to measure risks involved in an investment instrument. Standard deviation provides investors a mathematical basis for decisions to be made regarding their investment in financial market. Standard Deviation is a common term used in deals involving stocks, mutual funds, ETFs and others. Standard Deviation is also known as volatility. It gives a sense of how dispersed the data in a sample is from the mean.
I hope I answered correctly :)
Coleman uses his graphing calculator to find all of the solutions to the equation shown below.
23 + 3 = -24 + 4
What are ALL of the solutions to the equation, rounded to the nearest hundredth?
A.
x = 0.82 and 3.55
B. O x = -1.38 and 0.37
C.
x = 0.37 and 3.55
D.Ox=-1.38 and 0.82
Answer:
The correct option is;
D. x = -1.38 and 0.82
Please find attached the combined function chart
Step-by-step explanation:
The given equation is x³ + 3 = -x⁴ + 4
Plotting the equation using Excel, we have;
f(x) = x³ + 3, h(x) = -x⁴ + 4
x f(x) h(x)
-1.4 0.256 0.1584
-1.39 0.314381 0.26699
-1.38 0.371928 0.373261
-1.37 0.428647 0.477246
-1.36 0.484544 0.57898
Which shows an intersection at the point around -1.38
x f(x) h(x)
0.77 3.456533 3.64847
0.78 3.474552 3.629849
0.79 3.493039 3.610499
0.8 3.512 3.5904
0.81 3.531441 3.569533
0.82 3.551368 3.547878
0.83 3.571787 3.525417
Which shows the intersection point around 0.82
Therefore, the correct option is x = -1.38 and 0.82
From the graphing calculator the intersection point is given as
x = -1.3802775691 and 0.81917251339.
Clarence set his watch 16 seconds behind , and it falls behind 2 seconds every day . How many days behind has it been since Clarence last set his watch if the watch is 46 seconds behind
Answer:
15 days.
Step-by-step explanation:
46 - 16 = 30.
It falls 2 seconds behind each day so the number of required days
= 30 / 2 = 15.
Answer:
Step-by-step explanation:
15 days 16-40=30 the take 30/2= 15
Evaluate −12(−2). (1 point) 14 −14 −24 24
Answer:
24.
Step-by-step explanation:
−12(−2
= -12 * -2 ( Note - * - = +) so we have:
24 (answer).
is -7 a rational number
5. Jonathan and Victoria can finish a job in 13 days. Jonathan can do the job
himself in 26 days. if Victoria wanted to do the job alone, how long would it
take her?
6. If a certain job can be finished by 18 workers in 26 days. How many workers
are needed to finish job in 12 days?
.
7. A group of 40 workers can finish digging a tunnel in 12 days. how many
workers can finish the job in 8 days?
Answer:
about 8 workers will finish the job
Shamika knows she has been listening to a music playlist for 26 minutes when she looks at the clock showing the time below. What time did Shamika begin listening to the playlist?
Answer:
t = 5:26
Step-by-step explanation:
time after 26 min = 5:52
time before 5:52 after listening for 26 min
t = 5:52 - 0:26
t = 5:26 was the time when Shanika starts listening to a music.
Answer:
t = 5:26
Step-by-step explanation:
time after 26 min = 5:52
time before 5:52 after listening for 26 min
t = 5:52 - 0:26
t = 5:26
Someone lmk thank youuu
Answer:
please mark my answer brainliest
Step-by-step explanation:
=8 x cube + 27
=2 X whole cube + 3 whole cube
=(2x+3)(2 X whole square + 3 whole square -2× 2 X ×3 )
=(2x+3)(4x square +9-12x)
....thats all...if require more than use splitting midterm to get more appropriate answer
A triangle has vertices at (1,3),(2,-3), and (-1,-1). What is the approximate perimeter of the triangle? A. 16 B: 14 C: 15 D: 10
Answer:
B 14
explanation:
i did the math
The perimeter of the given triangle is 14 units, so the correct option is B.
How to get the perimeter of the triangle?
The perimeter of the triangle will be equal to the sum between the distances between the given points.
Remember that the distance between two points is (x₁, y₁) and (x₂, y₂) is:
[tex]d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex]
For the pair of (1,3), (2,-3): the distance is:
[tex]d = \sqrt{(2 - 1)^2 + (-3 - 3)^2} = 6.08[/tex]
For the pair (1, 3) , (-1, -1) the distance is:
[tex]d = \sqrt{(-1 - 1)^2 + (-1 - 3)^2} = 4.5[/tex]
For the pair (2, -3) and (-1, -1) the distance is:
[tex]d = \sqrt{(2 - (-1))^2 + (-3 - (-1))^2} = 3.6[/tex]
Then the total perimeter, rounded to the next whole number is:
6.08 + 4.5 + 3.6 = 14
So the correct option is B.
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Jacob spent $35.40 to fill up 15 gallons of gas in his pick-up truck. How much does 6 gallons cost?
Answer:
$14.16 for 6 gallons.
Step-by-step explanation:
35.40/15 = 2.36
2.36*6 = 14.16
The calorie count of a serving of food can be computed based on its composition of carbohydrate, fat, and protein. The calorie count C for a serving of food can be computed using the formula C = 6h + 11f + 7p, where h is the number of grams of carbohydrate contained in the serving, f is the number of grams of fat contained in the serving, and p is the number of grams of protein contained in the serving. Solve this formula for f, the number of grams of fat contained in a serving of food.
Answer:
see below (I hope this helps!)
Step-by-step explanation:
C = 6h + 11f + 7p
Get all non-f terms on one side:
C - 6h - 7p = 11f
Divide by 11:
f = [tex]\frac{C - 6h - 7p}{11}[/tex]
how do you break down 213 in times
Answer:2 hundred+1 tens+3 ones
Step-by-step explanation:
The sequence {an) is defined by ao = 1 and
An+1=2an +1 for n = 0,1,2,.... What is the value
of a4?
=======================================
Work Shown:
Use the value of a0 to find the value of a1. The idea is you double the previous value, and then add 1.
[tex]a_{n+1} = 2*(a_n) + 1\\\\a_{0+1} = 2*(a_0) + 1\\\\a_{1} = 2*(1) + 1\\\\a_{1} = 3\\\\[/tex]
Which is then used to find the value of a2. Follow the same process as before (double the previous value and then add 1).
[tex]a_{n+1} = 2*(a_n) + 1\\\\a_{1+1} = 2*(a_1) + 1\\\\a_{2} = 2*(3) + 1\\\\a_{2} = 7\\\\[/tex]
This is used to find a3
[tex]a_{n+1} = 2*(a_n) + 1\\\\a_{2+1} = 2*(a_2) + 1\\\\a_{3} = 2*(7) + 1\\\\a_{3} = 15\\\\[/tex]
Finally we can now find a4
[tex]a_{n+1} = 2*(a_n) + 1\\\\a_{3+1} = 2*(a_3) + 1\\\\a_{4} = 2*(15) + 1\\\\a_{4} = 31\\\\[/tex]
Recursive sequences like this aren't too bad if n is small, but as n gets larger, things become more tedious. For those cases, its best to try to find a closed form equation. If not, then the next best thing is using a spreadsheet to automate the process.
Classify the numbers as rational or irrational.
6
√2.6
√2+6
Step-by-step explanation:
[tex] \sqrt 2, \: \sqrt 2. 6 \: \& \: \sqrt 2 + 6[/tex] are irrational and 6 is the only rational number.
40 ➗ [24 - 4 x (2 + 3) ]
What is the value of this expression?
Answer: this is your answer
10
_____
6-5x
Answer:
1.7-20x OR 10/6-5x
Step-by-step explanation:
40÷(24-4x(2+3))
first you add the last set of ()
40÷(24-4x(5))
then you multiply by 4x
40÷(24-20x)
since you can't subtract those two you do this
40÷24-20x
divide 40 and 24
you get 1.66666667 then you round up
1.7-20x
ORyou put 40/24-20x
divide the top and the bottom by 4
(40÷4)/(24÷4) -(20x÷4)
and your answer will be
10/6-5x
you are building a new house and need to pour 1200 cubic feet of concrete for the foundation. the concrete truck delivers concrete by the cubic yard. how much concrete do you need to buy from the concrete company?
Answer:
400 cubic yards
Step-by-step explanation:
There are three cubic feet in each cubic yard
0.07 is 10 times as great as ? A.0.1 B.0.7 C.0.001 D.0.007
Answer:
D. 0.007
Step-by-step Explanation:
0.07= 10 x
= 0.07/ 10
= 0.007
In the accompanying diagram, a right circular cone is carved out of a solid foam cylinder and discarded. What is the volume of the foam remaining in the cylinder?
A. 150π cubic units
B. 125π cubic units
C. 100π cubic units
D. 50π cubic units
Answer:
100π cubic units is left
Step-by-step explanation:
πr²h - 1/3πr²h
π(5)²(6) - 1/3π(5)²(6)
150π - 50π = 100π
The volume of the foam is 100π cubic units remaining in the cylinder.
Given,
Radius of cone (r) = 5
Height of cone (h) = 6
What is the volume of a cone?The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.
∵ The volume of the cone (V )= 1/3πhr²
To determine the volume of the foam remaining in the cylinder
Subtract the volume of the cone into the volume of the cylinder
⇒ πr²h - 1/3πr²h
Substitute the values of h and r,
⇒ π(5)²(6) - 1/3π(5)²(6)
⇒ 150π - 50π
⇒ 100π
Hence, The volume of the foam is 100π cubic units remaining in the cylinder.
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Consider the polynomial 6x4 + 24x3 − 72x2. What is the greatest common factor (GCF) of the terms of the polynomial?
Answer:
24x
Step-by-step explanation:
=6x×4+24x×3-72x
=24x+24×3x-72x
=24x+72x-72
=24x
What is the solution to this equation 34(x+8)=12(x−6)
Answer:
x = - 172*11
Step-by-step explanation:
7p − p = 18 2) −5n − 4n = −9
Answer:
[tex] \boxed{ \bold{ \sf{ \boxed{ p = 3}}}} [/tex][tex] \boxed{ \bold{ \sf{ \boxed{n = 1}}}}[/tex]
Step-by-step explanation:
1. [tex] \sf{7p - p = 18}[/tex]
Collect like terms
⇒[tex] \sf{6p = 18}[/tex]
Divide both sides of the equation by 6
⇒[tex] \sf{ \frac{6p}{6} = \frac{18}{6} }[/tex]
Calculate
⇒[tex] \sf{p = 3}[/tex]
2. [tex] \sf{ - 5n - 4n = - 9}[/tex]
Collect like terms
⇒[tex] \sf{ - 9n = - 9}[/tex]
Divide both sides of the equation by -9
⇒[tex] \sf{ \frac{ - 9n}{ - 9} = \frac{ - 9}{ - 9} }[/tex]
Calculate
⇒[tex] \sf{n = 1}[/tex]
Hope I helped!
Best regards!!
26.9 microgram/milliliter to hectograms/deciliter
Answer:
.0000269 hectograms/ deciliter
2.69 * 10^e-5 hectograms/ deciliter
Step-by-step explanation:
micro grams to hectograms
10^8 micrograms = 1 hectogram
milliliters to deciliter
100 milliliters = 1 deciliter
Using conversion factors
26.9 microgram 1 hectogram 100 milliliters
----------------------- * --------------------------- * ---------------------
milliliter 10^8 micrograms 1 deciliter
2690 hectograms
---------------------------
10^8 deciliters
.0000269 hectograms/ deciliter
2.69 * 10^e-5 hectograms/ deciliter
Two years ago ,a woman was 7 times as old as her daughter,but in 3 years time ,she would be 2 times as old as the girl,how old are they now?.
Let present age of women and her daughter be x and y respectively.
According to the question,
Case 1 :
Two years ago,
Woman age = ( x - 2 ) years
Her daughter age = ( y - 2 ) years
Woman was 7 times old as her daughter. [ Given ]
x - 2 = 7 ( y - 2 )
=> x - 2 = 7y - 14
=> x - 2 + 14 = 7y
=> x + 12 = 7y ....( i )
Case 2 :
After Three years ,
Woman age = x + 3
Her daughter age = y + 3
she would be 4 times old as the girl. [ Given ]
x + 3 = 4 ( y + 3 )
=> x + 3 = 4y + 12
=> x = 4y + 12 - 3
=> x = 4y + 9....( ii )
Now,
★ Substituting the value of x = 4y + 9 from equation ( ii ) in equation ( i ),we get
x + 12 = 7y
=> 4y + 9 + 12 = 7y
=> 21 = 7y - 4y
=> 21 = 3y
=> 3y = 21
=> y = 21/3
=> y = 7
And,
x = 4y + 9
★ Substituting the value of y in equation ( ii ), we get
x = 4 × 7 + 9
x = 28 + 9
x = 37
Hence, the present age of women is 37 years and her daughter age is 7.
the current age of the daughter is 3 years old, and the current age of the woman is 9 years old.
Let's denote the current age of the daughter as "D" and the current age of the woman as "W".
From the given information:
1. Two years ago, the woman was 7 times as old as her daughter:
W - 2 = 7(D - 2)
2. In three years time, the woman would be 2 times as old as the girl:
W + 3 = 2(D + 3)
We now have a system of two equations with two unknowns. Let's solve this system of equations:
From equation 1, we can rewrite it as:
W = 7(D - 2) + 2
Substituting this expression for W in equation 2, we have:
7(D - 2) + 2 + 3 = 2(D + 3)
Simplifying the equation:
7D - 14 + 2 + 3 = 2D + 6
Combine like terms:
7D - 9 = 2D + 6
Subtract 2D from both sides:
7D - 2D - 9 = 6
Combine like terms:
5D - 9 = 6
Add 9 to both sides:
5D = 15
Divide both sides by 5:
D = 3
Now that we know the daughter's current age (D = 3), we can substitute it back into equation 1 to find the woman's age:
W = 7(D - 2) + 2
W = 7(3 - 2) + 2
W = 7(1) + 2
W = 7 + 2
W = 9
Therefore, the current age of the daughter is 3 years old, and the current age of the woman is 9 years old.
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reduce to simplest term 44/4
Answer:
11
Step-by-step explanation:
44/4 = 11
4/4 = 1
then:
44/4 = 11/1 = 11
The sum of a number and its square is 42. Which equation can be used to find the two numbers for which this is
true?
x2 + x = 42
x2 + 2x = 42
x²+x+42=0
x² + 2x + 42=0
Answer:
x2 + x = 42
Step-by-step explanation:
x = nhmber
x² = its square
then:
The sum of a number and its square is 42 is:
x² + x = 42
Simplify 5/96 - 7/54
Answer:
The answer is
[tex] - \frac{67}{864} [/tex]Step-by-step explanation:
[tex] \frac{5}{96} - \frac{7}{54} [/tex]To solve first find the LCM of the denominators
That's
The LCM of 96 and 54 is 864
So we have
[tex] \frac{5}{96} - \frac{7}{54} = \frac{5(9) - 7(16)}{864} [/tex][tex] = \frac{45 - 112}{864} [/tex]We have the final answer as
[tex] = - \frac{67}{112} [/tex]Hope this helps you