Answer:
[tex]t = - \frac{1}{2} b + \frac{5}{2} [/tex]
A car pulls forward 35 feet in 7 seconds, and then stops and sits still for 4 seconds, and then pulls backward 21 feet in 5 seconds. a) What is the distance that the car moved in the full 16 seconds? b) What is the total displacement of the car in the full 16 seconds? c) What are the average speeds in the first, second, and third parts of the car’s motion? d) What is the car’s average speed during the full 16 seconds? e) What is the car’s average velocity during the full 16 seconds?
a) The total distance covered is 56 feet
b) The total displacement is 14 feet
c) The average speed in the first, second, and third parts of the car’s motion are; 5 feet/sec, 0 feet/sec and 4.2 feet/sec
d) The average speed of the car is 3.5 feet/sec
e) The average velocity of the car is 0.875 feet/sec
What is the displacement?We must understand that the distance is the difference between two points but the displacement is the distance between two points in a definite direction. This implies that the distance is a scalar quantity while the distance is a vector quantity. Being a vector quantity means that when we are computing the displacement that we must take into account the direction of the motion and this also applies to the calculation of the velocity of the car.
Let us now carry pout the calculations;
a) Total distance = 35 feet + 21 feet = 56 feet
b) Total displacement = 35 feet - 21 feet = 14 feet
c) Average speed of the first, second, and third parts of the car’s motion;
i) 35 feet / 7 seconds = 5 feet/sec
ii) 0 feet/sec ( it sat still)
iii) 21 feet/5 seconds = 4.2 feet/sec
d) The cars average speed = 56 feet/16 seconds = 3.5 feet/sec
e) Average velocity = 14 feet/ 16 seconds = 0.875 feet/sec
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factor out the greatest common factor (5r-6)(r+3) - (2r-1)(r+3)
The factor (r + 3) is common. Then the greatest common factor will be (r + 3).
What is the greatest common factor?Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).
The expression is given below.
⇒ (5r - 6)(r + 3) - (2r - 1)(r + 3)
In both terms, the factor (r + 3) is common. Then the greatest common factor will be (r + 3). Then the expression will be
⇒ (5r - 6)(r + 3) - (2r - 1)(r + 3)
⇒ [(5r - 6) - (2r - 1)](r + 3)
⇒ (3r - 5)(r + 3)
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[tex] \rm\sum_{n = 0}^ \infty \bigg( - \frac{1}2 \bigg)^{n} \frac{ \Gamma ( \frac{1 + n}{2} )}{ \Gamma(1 + \frac{n}2) } \\ [/tex]
Let [tex]S[/tex] be the sum. Introduce a factor of [tex]\Gamma\left(\frac12\right)=\sqrt\pi[/tex] to rewrite the summand as a beta function integral. Then in the sum, interchange it with the integral, and [tex]S[/tex] reduces to a simple integral.
[tex]\displaystyle S = \sum_{n=0}^\infty \left(-\frac12\right)^n \frac{\Gamma\left(\frac{n+1}2\right)}{\Gamma\left(\frac n2+1\right)}[/tex]
[tex]\displaystyle . ~~ = \frac1{\sqrt\pi} \sum_{n=0}^\infty \left(-\frac12\right)^n \, \mathrm{B}\left(\frac n2+\frac12, \frac12\right) \\\\ ~~~~ = \frac1{\sqrt\pi} \sum_{n=0}^\infty \left(-\frac12\right)^n \int_0^1 \frac{t^{n/2}}{\sqrt t \sqrt{1-t}} \, dt \\\\ ~~~~ = \frac1{\sqrt\pi} \int_0^1 \frac{dt}{\sqrt t \sqrt{1-t}} \sum_{n=0}^\infty \left(-\frac{\sqrt t}2\right)^n \\\\ ~~~~ = \frac2{\sqrt\pi} \int_0^1 \frac{dt}{\sqrt t\sqrt{1-t}\left(\sqrt t+2\right)}[/tex]
Substitute [tex]u=\sqrt t+2[/tex] and [tex]du=\frac{dt}{2\sqrt t}[/tex].
[tex]\displaystyle S = \frac4{\sqrt\pi} \int_2^3 \frac{du}{u\sqrt{-(u-1)(u-3)}}[/tex]
Now substitute [tex]u=1+\frac2{1+t^2}[/tex] and [tex]du=-\frac{4t}{(1+t^2)^2}\,dt[/tex] - this comes from an Euler substitution of the form [tex]\sqrt{a(x-\alpha)(x-\beta)}=(x-\alpha)t[/tex]. [tex]S[/tex] reduces drastically to a trivial arctangent integral.
[tex]\displaystyle S = \frac8{\sqrt\pi} \int_0^1 \frac{dt}{t^2+3} \\\\ ~~~~ = \frac8{\sqrt\pi} \cdot \frac\pi{6\sqrt3} = \boxed{\frac43\sqrt{\frac\pi3}}[/tex]
An object is moving at a speed of 360 kilometers per hour. Express this speed in miles per day. Round your answer to the nearest whole number.
We get the speed of the object as 5365 miles / day after rounding off.
We are given that an object is moving at a speed of 360 kilometers per hour.
We know that:
1 km = 0.621 miles.
So, 360 km will be:
360 km = 223.56 miles.
Also, we know that:
we have 24 hours in 1 day.
1 day = 24 hours.
1 hour = 1 / 24 day.
Re-writing the speed of the object, we get that:
223.56 miles in 1 / 24 day
That is:
5365.44 miles / day.
Rounding off:
= 5365 miles / day.
Therefore, we get the speed of the object as 5365 miles / day after rounding off.
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3. Ages of Accountants. The average age of the accountants at Three Rivers Corp. is 25 years,
with a standard deviation of 4 years; the average salary of the accountants is $30,500, with a
standard deviation of $4500. Compare the variations of age and income.
The age of accountant is more variable than salary.
What is standard deviation ?Standard deviation is the square of difference between the sets of data and mean.
Comparison for variation of data can be determined by coefficient of variation (C.V).
We know C.V = [tex]\frac{\sigma}{|\overline{x|}}[/tex] × 100.
First we are determining C.V for ages.
Where [tex]\sigma[/tex] = standard deviation and [tex]|\overline{x}|[/tex] = arithmetic mean or average.
∴ C.V for ages, where [tex]\sigma[/tex] = 4 and [tex]|\overline{x}|[/tex] = 25 years is
C.V = [tex]\frac{4}{25}[/tex] × 100.
C.V = 16.
[tex]C.V_a_g_e[/tex] = 16%.
Now C.V for salary,
where [tex]\sigma[/tex] = 4500 and [tex]|\overline{x}|[/tex] = 30500.
C.V = [tex]\frac{4500}{30500}[/tex] × 100.
C.V = [tex]\frac{4500}{305}[/tex].
[tex]C.V_s_a_l_a_r_y =[/tex] 14.75 %.
So, the coefficient of variation of age is more than that of salary.
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A line passes through the points (-20, 4) and (-15, 8).
Calculate the slope of the line - simplify answer if possible. (If the slope is undefined, enter "DNE")
Then, write the equation of the line.
Answer:
The slope is 4/5
y = 4/5x + 20
Step-by-step explanation:
Slope:
Change in y over the change in x
(4 - 8) / -20 - -15
-4 / -20 + 15
-4 /-5
4 / 5
Equation of the line:
You could use either point given. I am going to use the point (-20,4) I will use -20 for x and 4 for y. I will use 4/5 as the slope. I will need to solve for the y-intercept
y = mx + b
4 = (4/5)(-20) + b
4 = -16 + b Add 16 to both sides
20 = b
The equation will be
y = 4/5x + 20
Use the phrase below to answer the following questions.
The sum of -15y and 16y is −4.
Translate the phrase into an algebraic equation.
Now, use your equation to solve for y.
y =
The translation of the phrase The sum of -15y and 16y is −4 is
-15y + 16y = -4 and the value of y is -4.
What is an algebraic equation?An algebraic equation is written in the form of variables and constants and we combine these variables and constants with arithmetic operations.
In the given question there is a statement The sum of -15y and 16y is −4 and we have to express it in form of numerical and solve for y or find the value of y.
∴ The sum of -15y and 16y is −4 can be expressed numerically as,
-15y + 16y = -4.
y = -4.
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Harold’s Men’s Clothing sells a suit on clearance. The suit was originally marked down 40% off its retail-selling price, but the suit did not sell. Harold’s Men’s Clothing further marked down the suit 60% below the first discount. What was the original price of the suit before markdowns if the suit finally sold for $125?
The original price of the suit before markdowns will be $520.83.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
Le's suppose the original price was x dollars.
Now, the first discount of 40%
40% of x = 0.40x
Retail price = x - 0.40x = 0.60x
The second discount is 60% on the first retail price
60% of 0.60x = 0.60×0.60x
⇒ 0.36x
Final retail price = 0.60x - 0.36x
0.24x = 125
x = 520.83
Hence "The original price of the suit before markdowns will be $520.83".
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30 ones, 2 thousands, 4 hundred thousands, 60 tens and 100 hundreds what number am I?
Answer:
602,630
Step-by-step explanation:
Does anyone understand this?
Answer: B.
Step-by-step explanation:
the goal of the question is to make <AZB ≈ (around) <AYB. Answer b is the only one that makes sense because in the first answer triangle AYB is obtuse and much wider than triangle AZB. While in answer c, triangle AYB is acute and way too small to be around triangle AZB. In answer b, the angles are around the same even though one triangle is slightly larger than the other.
Mrs. Lin asked her students to
write a sequence with a common
ratio of 5 where a₁ is negative. Who
correctly completed the task?
KORY
-1, 5, -25, 125,
REID
-3, -15, -75,-375,..
KEISHA
-10,-5, 0, 5, 10,
ALLIE
2, 10, 50, 250,
Answer:
REID: -3, -15, -75,-375,..Step-by-step explanation:
If a GP has a positive common ratio and negative first term, it means all its terms are negative since formed by a product of positive and negative numbers.
We can only see one sequence with all negative terms and common ratio of 5, this is REID's.
how many cubic feet water will aquarium A hold 16ft and 8ft
Answer:
128 feet
Step-by-step explanation:
8*16 is 128 feet
through: (1,-1), slope = -3/5
Answer:
equation : 3x + 5y + 2 = 0
Step-by-step explanation:
y - y1 = m (x - x1)
y - (-1) = -3/5 ( x - 1 )
5(y + 1) = -3(x - 1)
5y + 5 = -3x + 3
3x + 5y + 2 = 0
Determine the amplitude or period as requested.
Amplitude of y = negative one-third sine x
a.
Negative one-third
b.
StartFraction pi Over 3 EndFraction
c.
One-third
d.
3
The amplitude of the function is 1/3
How to determine the amplitude of the function?The function is given as:
y = negative one-third sine x
Rewrite properly as
y = -1/3sin(x)
A sine function is represented as:
y = Asin(x)
And the amplitude is
Amplitude = |A|
In y = -1/3sin(x), we have
A = -1/3
So, we have
Amplitude = |-1/3|
Evaluate
Amplitude = 1/3
Hence, the amplitude of the function is 1/3
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Factor completely 2x³+4x²+ 6x +12.
O20x²+2x²+3x+6)
O (2x²+6)(x+2)
O(x²+3)(2x + 4)
2[(x²+3)(x+2)] Skry
Answer: use the 'grouping method' to get your answer (answer choice 'B')
Step-by-step explanation:
Take your first two terms, 2x^3 and 4x^2 and find a GCF. In this case, 2x^2 can go into both terms. Your first side should look like this 2x^2(x+2).
Take your last two terms (6x+12) and find a GCF. In this case, your GCF is 6 because both terms can fit into 6. Your second side should look like this 6(x+2).
We know we did this problem correctly because we can see that both parenthesis state the same thing, which is (x+2).
Your equation after finding a GCF in both sets should look something like this; 2x^2(x+2)+6(x+2).
Now, combine the 2x^2 and 6 together to get (2x^2+6) in one parenthesis set. Your second should include ONLY ONE of the '(x+2)'s.
Your final answer should look like this; (2x^2+6)(x+2). Therefore, your answer choice is 'B'.
Hope this helps, dawg.
Reduce answers to lowest terms 5/9 + 1/10
The answer for the given question is 59/90
A fraction is said to be in lowest terms when the greatest common factor (GCF) of the numerator and denominator is 1. Now that this is in mind, let's continue to solve.
Given, 5/9+1/10 and we have to convert or reduce it into the lowest terms.
So, let's proceed to solve this question
First add 5/9 and 1/10 i.e.,
= 5/9+1/10
Taken LCM of 9 and 10 which comes out to be 90.
Then, adding, we get
= 50+9/90
= 59/90
59/90 is already in its lowest form because the numerator and denominator have no common factor other than 1. So it's already at its most basic level.
Therefore, 59/90 is the required answer.
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Find an equation of the line perpendicular to 3y=x+3 that passes through the point (5,8). Write the answer in slope-intercept form, y=mx+b, with all fractions written in the lowest terms.
Let the equation of the line perpendicular to line 3x+2y=16 is:-
2x - 3y = C. ………………(1)
Line (1) passes through the point (9,-2), therefore
2×9 - 3×(-2)= C
or, C = 24.
Thus, the required equation is:-
2x - 3y = 24.
or, 3y = 2y - 24.
or, y = (2/3).x + (-8). Answer.
Hi everyoneeee i just need one thing done
solve this in word form
1,900
There are two ways to say 1900 in word form.
1900 = nineteen hundred
1900 = one thousand, nine hundred
Both are equally valid.
Answer: one thousand nine hundred
Step-by-step explanation:
Distributive property 3(2x+7)
10.79 less then the product of 26 and x
Answer:
I believe it's 15.21x
Step-by-step explanation:
10.79 - 26 * x
10.79 - 26x =
15.21x
Someone answer this riddle in the photo
They still loose 100 dollars
Answer:
The store lost $100....
I had 7 bottles and 3 friends how much will be left
The number of bottles that would be left is 1
How to determine the number of bottles that would be left?The given parameters are
Number of Bottles = 7
Number of Friends = 3
Assume that the bottles are to be shared among the friends only
The number of bottles that would be left is
Bottles left = Number of Bottles % Number of Friends
This gives
Bottles left = 7%3
Evaluate the modulo operation
Bottles left = 1
Hence, the number of bottles that would be left is 1
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A loptop and 3 tablets cost $810. A laptop and 1 tablet cost $630. How much does one laptop cost? How much does one tablet cost?
Answer: Tablet costs $225
Laptop costs $135
Step-by-step explanation:
Laptop is = x
Tablet = T
x + 3t = 810
x + t = 360
x = 360 - t
360 - t + 3t =810
2t = 450
t = 225
x + 225 = 360
x = 135
A rectangular room is 2 times as long as it is wide, and its perimeter is 32 meters. Find the
dimension of the room.
L=?
W=?
Answer: l=32/3 meters
w=16/3 meters
Step-by-step explanation:
P=perimeter, l=length, w=width
P=2l+2w
32=2(2w)+2w
32=4w+2w
6w=32
w=32/6
w=16/3 meters
32=2l+2(16/3)
32=2l+32/3
(32=2l+32/3)*3
96=6l+32
6l=64
l=64/6
l=32/3 meters
What is the sum of the polynomials? Need help.
Answer:
(d) 9x² -12y² -11x
Step-by-step explanation:
The sum of polynomials (8x² -9y² -4x) and (x² -3y² -7x) is found by combining like terms.
Polynomial additionWhen simplifying the sum of polynomials, the distributive property comes into play. It lets you add and remove parentheses, recognizing that factors outside parentheses multiply each term inside parentheses.
(8x² -9y² -4x) + (x² -3y² -7x)
= 8x² -9y² -4x + x² -3y² -7x . . . . . eliminate parentheses
= (8 +1)x² +(-9 -3)y² +(-4 -7)x
= 9x² -12y² -11x
One machine can seal 360 packages per hour, and an older machine can seal 140 packages per hour. How many MINUTES will the two machines working together take to seal a total of 700 packages?
Answer:
84 minutes
Step-by-step explanation:
360 per hour = 6 per min
140 per hour = 2 1/3 per min
Both together do 8 1/3 per min.
In 3 minutes, both machines together do 25 packages.
700/25 = 28.
In 3*28 minutes, which is 84 minutes, both machines together seal 700 packages.
Thanks!
Ordered: 100mg. Available: 0.1g. How many tablets should be given? ________
Answer:
1 TABLET
Step-by-step explanation:
1 tablet should be given. The aim is to ensure that the amount of medicine you give matches what was prescribed. In order to do that, we must change either the amount we ordered or the amount that is available so that they are both measured in the same unit.
How many tablets should be given?To decide the number of tablets that ought to be given, we have to be change over the accessible sum from grams to milligrams.
Given:
Ordered: 100 mg
Available: 0.1 g
1 g = 1000 mg
Converting the available sum to milligrams:
0.1 g * 1000 mg/g = 100 mg
Since the available amount is equal to the ordered sum, you'd have to be give 1 tablet.
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XZ is the perpendicular bisector of segment WY. Solve for k. Enter a NUMBER only.
=====================================================
Explanation:
"bisect" means to "divide in half"
So segment WY is split into two smaller equal pieces.
Segments WX and XY are the same length
WX = XY
6k+8 = 11k-12
6k-11k = -12-8
-5k = -20
k = -20/(-5)
k = 4
Suppose you received a score of 91 out of 100 on exam 1. The mean was 79 and the standard deviation was 8. What score do you need on exam 2 to do equally well, if the mean is 60 and the standard deviation is 12?
You require the score of 78 to do equally well in exam 2.
To compare both the scores, we need to compute the z scores of both exams and then compare the values. The formula for z-score is:
Z = (X - μ)/σ
Where X = score obtained
μ = mean score
σ = standard deviation
For Exam 1:
Z = (91 - 79)/8
= 12/8
Z = 3/2
To perform similarly well on the second exam, let x equal z 3/2.
For Exam 2:
Z = (x - 60)/12
3/2 = (x - 60)/12
By cross multiplying we get
2(x - 60) = 12 * 3
x - 60 = 36 /2
x - 60 = 18
x = 18 + 60
x = 78
Therefore, Consequently, you must achieve a score of 78 to perform equally well in Exam 2.
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Approximately how many fencing is needed to enclose a secular pond with a diameter of 23 feet
The amount of fencing needed to enclose the secular pond is 72.22 feet
What are perimeters?The perimeter of a shape is the sum of the side lengths of the shape
For all regular quadrilaterals, you add up the side lengths to determine the area
How to determine the amount of fencing needed to enclose the secular pond?The given parameter is
Diameter, d = 23 feet
The radius is calculated as
r = d/2
So, we have
r = 23/2
This gives
r = 11.5 feet
The circumference of the circle is calculated as
C = 2pi r
So, we have
C = 2 * 3.14 * 11.5 feet
Evaluate the product
C = 72.22 feet
Hence, the amount of fencing needed to enclose the secular pond is 72.22 feet
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