Answer:
The bullet reaches its final velocity after 0.1 second.
Step-by-step explanation:
Velocity: The ratio of distance to the time that needs to cover the distance.
Acceleration: The change of velocity per unit time is called the acceleration of the object.
[tex]Acceleration=\frac{\textrm{Final velocity- initial velocity}}{Time}[/tex]
S.I unit is m/s².
C.G.S unit is cm/s².
Dimension: [LT⁻²]
An accelerometer is used to measure acceleration of an object.
Given that
The bullet accelerates from a stop to 1000 m/s to the east.
It accelerates at 10,000 m/s² in the same direction.
The initial velocity of the object is = 0 m/s
The final velocity of the object is = 1000 m/s
[tex]\therefore 10000=\frac{1000-0}{Time}[/tex]
[tex]\rightarrow Time = \frac{1000}{10000}[/tex]
[tex]\rightarrow Time = \frac1{10}[/tex]
[tex]\rightarrow Time = 0.1[/tex]
The bullet reaches its final velocity after 0.1 second.
Angle C is inscribed in circle O. AB is a diameter of circle O. What is the radius of circle O?
Answer:
6.5 units
Step-by-step explanation:
In circle with center O, AB is diameter.
[tex] \therefore m\angle ACB = 90°\\[/tex]
(Angle inscribed in a semicircle)
[tex] \therefore \: in\: \triangle ABC, \:AB \: is\: hypotenuse \\[/tex]
By Pythagorean theorem:
[tex]AB = \sqrt{ {12}^{2} + {5}^{2} } \\ = \sqrt{144 + 25} \\ = \sqrt{169} \\ AB \: = 13 \\ r = \frac{13}{2} = 6.5 \: units[/tex]
Kalvins mother tells him that the chance of a coin showing heads when he tosses it is 1/2. Does this mean that every time he tosses a coin twice,he will get one head and one tail? Explain
Answer:
No
Step-by-step explanation:
The probability simply refers to the chance of an event occurring. What this means is that when a coin is tossed once, the chance that we can get a head is 50%. This is simply just referring to the likelihood of the event happening.
Now for the first toss, there is a likelihood of 50%, for the second toss too there will be a likelihood of 50%.
This is different from the fact that for every 2 throws there must be a head showing up
Find the median, first quartile, third quartile, and the interquartile of the data set.
32,47,49,53,54,66,67,71,72
Answer:
54 = median
48 = 1st quartile
69 = 3rd quartile
21 = interquartile
Hope this helped!! :)
Answer:
54 = median
48 = 1st quartile
69 = 3rd quartile
Step-by-step explanation:
in what quradrant does the terminal side of 0 lie when tan 0 < 0 and sin 0 < 0
Answer:
Step-by-step expla0000000000000000000000000nation:
Assume you have sea water that weighs 64 lb/ft³ and contains 35 parts per thousand (0.0035) dissolved salt by weight. How many cubic feet of the sea water would you need to place in an exaporation basin to collect 125 lb of sea salt?
Answer:
558.036 lb
Step-by-step explanation:
Let x is the amount of the sea water to collect 125 lb of sea salt
As given: 64 lb/ft³ has 0.0035 dissolved salt by weight
So the formula to find out the amount of the sea water is:
64 lb/ft³ * 0.0035 *x ft³ = 125 lb
<=> x = [tex]\frac{125}{64*0.035}[/tex] = 558.036 lb
Hope it will find you well.
The wholesale price for a chair is $108. A certain furniture store marks of the wholesale price by 27%. Find the price of the chair in the furniture store. Round your answer to the nearest cent as necessary.
Answer:
The price of chair in furniture house is $137.16
Step-by-step explanation:
We are given the following in the question:
Wholesale price of chair = $108
Marked percentage = 27%
We have to find the price of the chair in the furniture store.
Increased price =
[tex]=27\%\times 108\\\\=\dfrac{27}{100}\times 108\\\\=29.16\$[/tex]
Price of chair in furniture house =
= Wholesale price + Increased price
[tex]=108 + 29.16\\=137.16\$[/tex]
Thus, the price of chair in furniture house is $137.16
You have $30 dollars saved up. Every week you spend $6 at the arcade. Write an equation in slope intercept form that shows how much money you have (y) after x weeks.
Answer:
y = -6x + 30
Step-by-step explanation:
The inicial value you have is $30, so this will be the value of y after 0 weeks, that is, x = 0
After one week, you spend $6, so you will have y = 30 - 6 = 24 when x = 1.
With these pair of values, we can find the linear equation:
y = ax + b
for x = 0, y = 30:
30 = a*0 + b
b = 30
for x = 1, y = 24:
24 = a*1 + 30
a = 24 - 30 = -6
So, our equation is:
y = -6x + 30
Penelope invested $32,000 in an account paying an interest rate of 7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 14 years?
Answer:
85263
Step-by-step explanation:
In Penelope's account $ 85262.6 would be there after 14 years.
What is Compound Interest ?The compound Interest is the interest you earn on Interest .
The formula for calculating the amount when the interest is compounded continuously
P = P₀[tex]\rm e^{rt}[/tex]
Penelope invested $32,000 in an account
interest rate of 7% compounded continuously.
After 14 years the amount will be
P = 32000 * [tex]\rm e^{0.07*14}[/tex]
P = $ 85262.6
Therefore $ 85262.6 would be in the account after 14 years.
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Ryan mows lawns in the summer. He charges $15 for every 1/2 hour of mowing. This is represented by the equation y = 15x, where y is the total amount Ryan charges and x is the number of 1/2 -hour sessions of mowing. If mr.smith lawn takes 2 hours to mow and mrs.jones lawn 3.5 hours to mow, how much more would Ryan charge mrs Jones then me.smuth
Answer:
$45 more
(but honestly I think I would spend longer mowing their lawns to try and make some more profit)
Step-by-step explanation:
Mr. Smith requires 4 1/2 hours.
Mrs Jones requires 7 1/2 hours.
7 - 4 = 3
3 * 15 = $45
To find the difference in charges between Mrs. Jones and Mr. Smith for mowing lawns, calculate the total amount charged by Ryan for each lawn and subtract the amount charged for Mr. Smith from the amount charged for Mrs. Jones. The difference in charges is $22.50.
Explanation:The question asks how much more Ryan would charge Mrs. Jones than Mr. Smith for mowing lawns.
To find the answer, we need to calculate the total amount charged by Ryan for each lawn and then subtract the amount charged for Mr. Smith from the amount charged for Mrs. Jones.
For Mr. Smith's lawn, the given information is that it takes 2 hours to mow. So, the total amount charged would be y = 15 * 2 = $30.
For Mrs. Jones' lawn, it takes 3.5 hours to mow. So, the total amount charged would be -
y = 15 * 3.5 = $52.50.
To find the difference in charges between Mrs. Jones and Mr. Smith, we subtract $30 from $52.50.
The difference is $22.50.
The number y of hits a new website receives each month can be modeled by y = 4060ekt, where t represents the number of months the website has been operating. In the website's third month, there were 11,000 hits. Find the value of k. (Round your answer to four decimal places.) k =
Answer: The value of k = 0.9031
Step-by-step explanation: The equation for calculating the number of hits has been given as y = 4060ekt, where y is the number of hits and t is the number of months the website has been operating.
The values for y and t has been determined already as given, (y = 11000 and t = 3) therefore we can substitute for the known values in order to calculate the value of the unknown, k.
y = 4060kt
11000 = 4060 x 3k
11000/(4060 x 3) = k
11000/12180 = k
0.9031198 = k
Rounded to four decimal places,
k = 0.9031
Bank A charger a 4$ service fee and $0.25 for each check written. Bank B charges $5 and $0.20 for each check written . How many checks does a person need to write each month for the two banks to charge the same amounts in fees. Which account would cost less if a person were to write 10 checks in a month?
Answer:
20 checks
Step-by-step explanation:
A ball is thrown directly upward from a height of 66 ft with an initial velocity of 2828 ft/sec. The function s(t)equals=minus−16tsquared2plus+2828tplus+66 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.
Answer:
Time taken to reach maximum height=0.875 seconds
Maximum height = 78.25 ft
Step-by-step explanation:
The function which models the height of the ball is given as:[tex]s(t)=-16t^2+28t+66[/tex]
The function s(t) reaches its maximum height at the axis of symmetry. For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex], the axis of symmetry occurs at [tex]x=-\frac{b}{2a}[/tex].
In s(t), a=-16, b=28
[tex]t=-\frac{28}{2(-16)}=0.875 seconds[/tex]
The ball reaches its maximum height after 0.875 seconds
(b)Maximum Height
Given [tex]s(t)=-16t^2+28t+66[/tex]
At t=0.875
[tex]s(0.875)=-16(0.875)^2+28(0.875)+66=78.25 ft[/tex]
Maximum height = 78.25 ft
Answer:
time: 0.875 seconds
maximum height: 18.25 feet
Step-by-step explanation:
The function that gives the height of the ball in feet after t seconds is:
s(t) = −16t^2 + 28t + 6
The inicial velocity is 28 ft/sec, and the inicial position is 6 feet.
So, to find the time when the ball reaches the maximum heigth, we need to find the vertix of the equation −16t^2 + 28t + 6.
We can use the following formula to find it:
t_vertix = -b/2a
where a and b are coefficients of the quadratic equation (in our case, a = -16 and b = 28).
So, we have that:
t_vertix = -28/(-32) = 0.875 seconds
To calculate the maximum height we just need to use this time in the equation of position:
s(0.875) = −16*(0.875)^2 + 28*0.875 + 6 = 18.25 feet
A used car costs $2,200 cash, or $600 down and $100 a month for 20 months. How much money do you save by paying cash?
Answer:
$400
Step-by-step explanation:
Cash = $2200
$600 + ($100*20) = 2600
$2600 - $2200 = 400
Explain how to rewrite the equation -2x - 6y = 18 in slope-intercept form.
Answer:
y = -1/3x -3
Step-by-step explanation:
-2x - 6y = 18
We want to solve for y since the slope intercept form is y =mx+b where m is the slope and b is the y intercept
Add 2x to each side
-2x-6y +2x = 2x+18
-6y = 2x+18
Divide each side by -6
-6y/-6 = 2x/-6 + 18/-6
y = -1/3x -3
This is in slope intercept form with the slope -1/3 and the y intercept -3
Answer:
[tex]y = - \frac{x }{ 3} - 3[/tex]
Step-by-step explanation:
-2x - y = 18
Add 2x to both sides.
-6y = 2x + 18
divide both sides by -6.
[tex]y = \frac{2x + 18}{ - 6} [/tex]
divide 2x + 18 by 6
[tex]y = - \frac{x }{ 3} - 3[/tex]
Kelly's recipe calls for 13 ounces of chicken. Her scale only measures in grams. Which of the following shows the number of grams of chicken, with the correct significant digits, that Kelly needs to include in her recipe in order to have 13 ounces? (1 ounce = 28.3495 grams)
A) 368.5435
B) 367.9
C) 369
D) 370
Answer:
A
Step-by-step explanation:
13 x 28.3495
Answer:
A
Step-by-step explanation:
1 ounce is 28.3495 grams and Kelly's recipe call for 13 ounces of chicken, so
13 x 28.3495 = 368.5435
The boundary of a field is a right triangle with a straight stream along its hypotenuse and with fences along its other two sides. Find the dimensions of the field with maximum area that can be enclosed with 1000 feet of fencing.(Must show work to back up your answer). A=1/2 bh
Answer:
[tex]500,500\text{ and }500\sqrt{2}[/tex] feet
Step-by-step explanation:
GIVEN: The boundary of a field is a right triangle with a straight stream along its hypotenuse and with fences along its other two sides.
TO FIND: Find the dimensions of the field with maximum area that can be enclosed with [tex]1000[/tex] feet of fencing.
SOLUTION:
Let the other two sides of triangle be [tex]x[/tex] and [tex]y[/tex]
such that, [tex]x+y=1000 \implies x=1000-y[/tex]
Area of triangle [tex]A=\frac{1}{2}\times base\times height=\frac{1}{2}\times x\times y[/tex]
Area of triangle[tex]A=\frac{1}{2}\times(1000-y)\times y=\frac{(1000y-y^2)}{2}[/tex]
to maximize area, put [tex]\frac{d\ A}{d\ y}=0[/tex]
[tex]\implies 500-y=0[/tex]
[tex]\implies y=500\text{ feet}[/tex]
other side [tex]x=1000-y=500\text{ feet}[/tex]
[tex]\text{hypotenuse}^2=x^2+y^2[/tex]
[tex]=500^2+500^2\implies \text{hypotenuse}=500\sqrt{2}[/tex]
dimension of triangle are [tex]500,500\text{ and }500\sqrt{2}[/tex] feet
The problem is solved by using the optimization strategy in mathematics. The maximum area of the field is obtained when the triangular field is an isosceles right triangle with base 500 ft and the hypotenuse side 250 ft each.
Explanation:This problem involves optimization in mathematics. In a right triangle with hypotenuse (h) and other two sides as base (b) and height (h), we know that the hypotenuse is the longest side. The Pythagorean theorem applies which states that h² = b² + h².
Given that the total length of the fences is 1000 ft, we know that b + h + h = 1000. We then solve for h and substitute it into the area formula, A = 1/2 bh. We get a quadratic function upon simplification, and we maximize the function to get the base and the height.
Using the strategy of setting the derivative equal to zero, the dimensions that maximize the area are found to be base b = 500 ft and the two equal sides h = 250 ft each which form the hypotenuse. Therefore, the field will have it's maximum area when it's a isosceles right triangle.
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A car's fuel efficiency is measured by the distance it can drive per a single unit of fuel. A common unit for efficiency is km/1, kilometers per liter of fuel. C(S) models the fuel efficiency of a certain car as a function of the car's speed S (in kilometers per hour). Match each statement with the feature of the graph that most closely corresponds to it.
The feature of the graph that most closely corresponds to the number of gallons of gasoline necessary to fill an automobile gas tank is the y-axis. The feature of the graph that most closely corresponds to the mass of a textbook is the line or curve representing the fuel efficiency as a function of the car's speed. The feature of the graph that most closely corresponds to the time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h is the distance traveled.
Explanation:The feature of the graph that most closely corresponds to the number of gallons of gasoline necessary to fill an automobile gas tank would be the y-axis. The y-axis represents the fuel consumption or efficiency of the car, which is measured in kilometers per liter (km/1).
The feature of the graph that most closely corresponds to the number of cm in 2 m would be the x-axis. The x-axis represents the speed of the car in kilometers per hour (km/h). It shows the relationship between the car's speed and its fuel efficiency.
The feature of the graph that most closely corresponds to the mass of a textbook would be the line or curve representing the fuel efficiency as a function of the car's speed. This line or curve shows how the car's efficiency changes as its speed varies.
The feature of the graph that most closely corresponds to the time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h would be the distance traveled. The distance traveled is an important factor in determining the car's fuel efficiency.
1+1=
2+2=
5x7-2+5=
7000+3+67+90=
Step-by-step explanation:
[tex]1+1=2 \\
2+2=4 \\
57-2+5=60 \\
7000+3+67+90=7160[/tex]
Answer:
7160
Step-by-step explanation:
1+1=2
2+2=4
5x7-2+5=5x7+3
7000+3+67+90+7160
A car's fuel efficiency is measured by the distance it can drive per a single unit of fuel. A common unit for efficiency is km/1, kilometers per liter of fuel. C(S) models the fuel efficiency of a certain car as a function of the car's speed S (in kilometers per hour). Match each statement with the feature of the graph that most closely corresponds to it.
Answer: Y-intercept: When the car doesn’t move...
Relative max or min: The most efficient...
Increasing or decreasing interval: As the car accelerates...
Step-by-step explanation:
The parameters are matched and shown below..
What is the of [y] - intercept of a graph?The [y] - intercept of a graph is the point where the graph cuts the [y] axis.
We have a curve that models the fuel efficiency of a certain car as a function of the car's speed.
The [y] - intercept of the graph would be at y = 0. This point represents the situation when the car does not have any fuel to move.
The increasing or decreasing value represents as car accelerates towards 55 Km/hr, it gets more efficient.
The relative maximum value represents that the most efficient the car can get is 20 Km/litre.
Therefore, the parameters are matched and shown above.
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Two plumbers charge different rates for service. The first plumber charges $100 for every service call plus $25 per hour of service. The second plumber charges $50 for every service call plus $50 per hour of service. After how many hours do the plumbers charge the same amount
After two hours the two plumbers will charge the same amount
Step-by-step explanation:Set up your equations
Plumber 1:
y = 25x + 100
Plumber 2:
y = 50x + 50
Set the two equal to each other and solve
25x + 100 = 50x + 50
-50 -50
25x + 50 = 50x
-25x -25x
50 = 25x
50/25 = 25x/25 <- Divide both sides by 25
x = 2
After two hours the two plumbers will charge the same amount
Sven observes a bird on top of a light pole. His eye level is 6 feet off of the ground. Sven is 48 feet from the pole. If the distance to the bird from Svens eyes is 50 feet, how tall is the pole?
The height of the pole is 20ft.
Step-by-step explanation:
Let the height of the pole be '(h+6)'
Distance between the pole and Sven = 48ft.
Height of Sven = 6 ft.
Distance between the bird and his eyes = 50 ft.
We can find the value of 'h' using pythogoras theorem,
h = √(2500-2304)
h = √(196)
h = 14 ft.
The height of the pole = h + 6
= 14 + 6
= 20ft.
The height of the pole is 20ft.
How do I solve this math problem you and your friend are selling magazine subscriptions for a fundraiser. After w weeks , you have sold (7w = 6) subsriptions and your friend has sold ( 9w = 2) subscriptions. Whats the diffrence written in simple expression form?
Answer:
The diffrence written in simple expression form is 40/63
Step-by-step explanation:
To solve for the difference normally you have to subtract your own subscription from that of your friends,
Let's perform this operation step wise
Now your subscription is
(7w = 6)
w=6/7
Your friends own is
( 9w = 2)
w=2/9
So the difference in simple form is
6/7-2/9
The LCM is 63 I.E 9*7=63
=54-14/63
=40/63
I JUST NRRD HELP ASAP WILL GIVE CROWN
Dom and Amad are playing catch on a grassy field. The field is rectangular in shape. Dom says he knows that it has a perimeter of 48 yards. Jack says he knows that it has a width of 24 feet.
What is the length of the field in feet?
ft
Answer:
48 feet
Step-by-step explanation:
Since 1 yard = 3 feet
Therefore, 48 yards = 3* 48 = 144 feet
[tex]P = 2(l + w) \\ 144 = 2(l + 24) \\ \frac{144}{2} = l + 24 \\ 72 = l + 24 \\ 72 - 24 = l \\ l = 48 \: feet[/tex]
Hence, length of the field is 48 feet.
Answer:
48 ft im pretty sure
Step-by-step explanation:
Let x^2+17x=-5 What values make an equivalent number sentences after completing the square? (Do not simply your answers)
Answer:
[TeX] (x+\frac{17}{2})^{2}=\frac{269}{4} [/TeX]
Step-by-step explanation:
Given the expression:
[TeX] x^2+17x=-5 [/TeX]
To complete the square,
First Step: Identify the Coefficient of x.
Coefficient of x=17
Second Step: Divide the coefficient of x by 2.
Third Step: Square your result from the second step.
This gives:
[TeX] (\frac{17}{2})^{2}[/TeX]
Fourth Step: Add your result to both sides if the equation.
[TeX] x^2+17x+(\frac{17}{2})^{2}=-5+(\frac{17}{2})^{2} [/TeX]
Fifth Step:Express the left hand side as a square
[TeX] (x+\frac{17}{2})^{2}=-5+(\frac{17}{2})^{2} [/TeX]
Sixth Step:Simplify the Right Hand Side
[TeX] (x+\frac{17}{2})^{2}=\frac{269}{4} [/TeX]
These are the values that make an equivalent number sentence.
How to find the slope of the line between (8,-2) and (-3,9)
Answer:
-x or -1xStep-by-step explanation:
you would find the slope by doing the change in y over the change in x. in your case, the change in y is 11 and the change in x is -11.
Answer:
Slope formula is y2-y1 over x2-x1
Once you find the slope you are going to need to put it into point slope form which is y-y1=m(x-x1)
Step-by-step explanation:
9-(-2) divided by -3-8 is 11 over -11 which your slope is -1 m=-1
Then you use the point slope formula
y-(-2)=-1(x-8)
Then solve algebraically
Y+2=-1x+8
-2. -2
Y=-1x+6 , that is in slope-intercept form your m which is your slope is -1 and your b which is your y intercept is 6
So basically your answer is slope(m) which is -1.. hope this helps!!
What is 12 divided by 220
Answer:
0.0545454545455
Step-by-step explanation:
1. The length of each leg of an isosceles right triangle is 13 cm. What is the length of the hypotenuse?
Answer:
Step-by-step explanation:
For right triangles, we can use the Pythagorean theorem. This means that a2+b2 = c2. In this problem, a and b are the given side lengths of the triangle. This means that a=b=13. To solve this problem, we plug in 13 to the equation above and solve for c.
132 + 132 = c2
169+169 = c2
338 = c2
square root(338) = c
c = 18.38
Answer:18.38
Step-by-step
13^2 +13^2=338
square root 338
=18.38
What is the solution to the system of equations 6x+2y=6 7x+3y=5
Answer:
(x,y)=(2,-3)
Step-by-step explanation:
6x+2y=6
7x+3y=5
Multiply both sides by 3
18x+6y=18
7x+3y=5
Multiply both sides by -2
18x+6y=18
-14x-6y=-10
Eliminate one variable by adding the equations
4x=8
x=2
Substitute the value of x to get y
6(2)+2y=6
y=-3
x=2
y=-3
The solution to the system of equations 6x+2y=6 and 7x+3y=5 is x = 2 and y = -3.
The solution to the system of equations 6x+2y=6 and 7x+3y=5 involves finding the values of x and y that satisfy both equations simultaneously.
First, let's multiply:
3(6x + 2y) = 3(6)
=> 18x + 6y = 18
2(7x + 3y) = 2(5)
=> 14x + 6y = 10
Next, we subtract the second equation from the first:
18x + 6y - (14x + 6y) = 18 - 10
4x = 8
x = 2
Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. For instance, substituting x into the first original equation:
6(2) + 2y = 6
12 + 2y = 6
2y = 6 - 12
2y = -6
y = -3
The solution to the system of equations is x = 2 and y = -3.
Carlo rode his bike from his house to his friend Kevin’s house from there he rode to a video game store then he Road 3.2 km from the video game store back to his house that it was in the grid so the path Carlo trouble how many kilometers deCarlo ride his bike
Answer: 13.7
Step-by-step explanation:
The total distance Carlo travelled form his house to Kelvin's house to the game store and back to his house is 13.7 km.
How to calculate distance from the graph?Using the distance formula, we can caulate the distance he rode from his house to Kelvin's house and then to the video game store.
Therefore,
d = √(y₂ - y₁)²+(x₂- x₁)²
Hence,
(0, 0)(2.5, 6)
Distance from his house to Kelvin's house = √(6- 0)²+(2.5 - 0)²
Distance from his house to Kelvin's house = √36 + 6.25 = 6.5 km
Therefore,
(2.5, 6)(2.5, 2)
Distance from Kelvin's house to game store = √(2- 6)²+(2-5 - 2.5)²
Distance from Kelvin's house to game store = √16 = 4 km
Hence,
Total distance travelled = 6.5 + 4 + 3.2 = 13.7 km
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PLZ HELP ASAP 20 POINTS
Step-by-step explanation:
A (the first one)
.............
The upside down U means intersection, which would be the area the two circles overlap.
X’ and y’ would be opposite, so the area not in x or y.
The area would be outside the circles
The answer would be picture b