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Related Questions
On a highway, Nick's car uses 12.5 gallons of gas to travel 240 miles. The gas tank in Nick's car holds 20 gallons of gas. How far can Nick's car travel on a highway using a full tank of gas?
Answers
20 : x
[tex]12.5x = 4800 \\ x = 384[/tex]
Answer : Nick's car can travel 384 miles using a full tank of gas.
Hope this helps. - M
Answer:
Nick's car can travel 384 miles using a full tank of gas.
Step-by-step explanation:
In how many different ways can the letters of the word china be arranged
Answers
5!= 5*4*3*2*1
5!=120 different options
Phil is offered a 3-year contract with a law firm. His first year earnings would be $81,000 with an annual raise of 15%.
What would Phil's total earnings be over the term of the contract?
Enter your answer, rounded to two decimal places, in the box.
Answers
Second year: 1.15($81000) = $93150
Third year: 1.15($93150) = $107122.50
Add these three together to get Phil's total salary over the 3 years of his contract.
Phil is offered a 3-year contract with a law firm. His first-year earnings would be $81,000 with an annual raise of 15%. Phil's total earnings would be over the term of the contract is $281272.5.
What is addition?The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
Phil is offered a 3-year contract with a law firm. His first-year earnings would be $81,000 with an annual raise of 15%.
First year
= $81000
Second year
1.15 x ($81000)
= $93150
Third year
1.15 x ($93150)
= $107122.50
Phil's total earnings would be over the term of the contract
= $81000 + $93150 + $107122.50
= 281272.5
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PLEASE HELP!!! ASAP!!!!!!!!!!!!!!! 10 POINTS
Expand the number 1800 into its corresponding exponential form.
2^3 · 3^2 · 5^2
9^2 · 100
8 · 9 · 25
2^2 · 3^3 · 5^2
Select expression equal to ^3√320
4
4^3√5
5^3√4
5^3√5
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[tex]\sqrt[3]{320}\\\\320|2\\160|2\\.\ 80|2\\.\ 40|2\\.\ 20|2\\.\ 10|2\\.\ \ 5|5\\.\ \ 1|\\\\320=2\cdot2\cdot2\cdot2\cdot2\cdo2\cdot5=2^3\cdot2^3\cdot5=2^3\cdot2^3\cdot\\\\\sqrt[3]{320}=\sqrt[3]{2^3\cdot2^3\cdot5}=\sqrt[3]{2^3}\cdot\sqrt[3]{2^3}\cdot\sqrt[3]{5}=2\cdot2\sqrt[3]{5}=4\sqrt[3]5\\\\Answer:\ \boxed{\sqrt[3]{320}=4\sqrt[3]{5}}[/tex]
They all have factors that can be smaller so
8= 2^3
3=3^2
25= 5^2
So they answer is 2^3 x 3^2 x 5^5
Silvia wants to retire at 65 and live on $40,000 a year. How much does she need to save to ensure that her retirement funds last until she is 85?
Select the best answer from the choices provided.
$800,000 because she will need to save for 20 years times $40,000
more than $800,000 because taxes and inflation will increase the value of her savings
less than $800,000 because returns will continue to increase the amount in her savings even after retirement
more than $800,000 because compound return will reduce her savings
Answers
Answer:
$800,000 because she will need to save for 20 years times $40,000
Step-by-step explanation:
Silvia wants to retire at 65 and live on $40,000 a year.
She wants to live till 85 and retire at 65 years.
So, number of years to save = [tex]85 -65= 20[/tex]
And she needs to save [tex]40000\times20=800000[/tex]
Hence, she must save 800,000.
Evaluate the expression
A. arctan ( - \sqrt{3} )
B. Arctan ( - \sqrt{3} )
Pls help i need this asap!
Answers
[tex]\tan x=-\sqrt3[/tex]
where [tex]x[/tex] lies in what you might call the "principal branch". That is, [tex]\arctan x[/tex] is bounded below by [tex]-\dfrac\pi2[/tex] and above by [tex]\dfrac\pi2[/tex], so it's only a valid inverse of [tex]\tan x[/tex] if we restrict the domain of [tex]\tan x[/tex] to [tex]-\dfrac\pi2<x<\dfrac\pi2[/tex].
In other words, [tex]x[/tex] is some angle whose terminus lies in either the first or fourth quadrant (I'm assuming you're at least a little familiar with the typical unit circle diagrams used in trig). The only value of [tex]x[/tex] in this domain that satisfies the equation above is [tex]x=-\dfrac\pi3[/tex].
On the other hand, [tex]\mathrm{Arctan}(-\sqrt 3)[/tex] captures all possible values of [tex]x[/tex] that satisfy
[tex]\tan x=-\sqrt3[/tex]
First, we know that [tex]\tan(x+\pi)=\tan x[/tex] (in other words, [tex]\tan[/tex] has a period of [tex]\pi[/tex]), so in fact [tex]\tan(x+2\pi)=\tan(x-2\pi)=\cdots=\tan x[/tex] as well. In general, then, we know that [tex]x+n\pi[/tex] will be a valid solution to the equation above, where [tex]n[/tex] is any integer.
Earlier we found that [tex]\arctan(-\sqrt3)=-\dfrac\pi3[/tex], so in this case, [tex]\mathrm{Arctan}(-\sqrt3)=-\dfrac\pi3+n\pi[/tex] for [tex]n\in\mathbb Z[/tex].
The requried both A and B refer to the same calculation, which is finding the inverse tangent of -√3. The result is -60 degrees or -π/3 radians.
A. The expression "arctan(-√3)" represents the inverse tangent function of the value -√3. The inverse tangent function returns an angle whose tangent is equal to the given value.
To evaluate arctan(-√3), we can use a calculator or reference table that provides trigonometric function values. In this case, the value is approximately -60 degrees or -π/3 radians.
B. The expression "Arctan(-√3)" is the same as "arctan(-√3)" and represents the inverse tangent function of -√3. The uppercase "Arctan" notation is commonly used in mathematical literature and calculators to represent the inverse tangent function.
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The length of a rectangle is 5 yd less than three times the width, and the area of the rectangle is 28 yd2 . find the dimensions of the rectangle.
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The formula for the area of a rectangle is A = lw. Substitute, so then it's 28 = (3x-5) * x, and you evaluate.
Hope this helps you! And rate so I can see if I did well!
The dimensions of the rectangle are width = 4 yds and length = 7 yds.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
We have been given that the length of a rectangle is 5 yds less than three times the width,
The area of the rectangle is 28 yds square.
Let the width of the rectangle is x
So the length of the rectangle = 3x - 5
The area of a rectangle = x × (3x - 5)
28 = 3x² - 5x
3x² - 5x - 28 = 0
(3x + 7)(x - 4) = 0
3x + 7 = 0 and and x - 4 = 0
x = -7/3 and x = 4
Take x = 4 as the width
So the length of the rectangle = 3(4) - 5 = 12 - 5 = 7
Therefore, the dimensions of the rectangle are width = 4 yds and length = 7 yds.
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Solve for x in the image below
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Answer : x = 8
Hope this helps. - M
The value of x in the equation given is 8
Using the equations given for our Calculation;
7/8 - 1/x = 3/4Take the L.C.M of 8 and x ; which is 8x
(7x - 8) / 8x = 3/4
Now we cross multiply;
4(7x - 8) = 3 * 8x
open the bracket
28x - 32 = 24x
28x - 24x = 32
4x = 32
x = 8
Hence, the value of x = 8
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Please help me idk this
Answers
Answer:
1 13/20
Step-by-step explanation:
You want the total of distances walked to be the length of the hike:
2 1/10 + 1 1/4 + (left to walk) = 5
Then the amount left to walk is the difference ...
left to walk = 5 - 2 1/10 - 1 1/4
___
You are expected to know how to do arithmetic with mixed numbers, and/or to be able to use a calculator for the purpose.
5 - 2 1/10 - 1 1/4
= (5 -2 -1/10) - 1 1/4
= 2 9/10 - 1 1/4
= (2 -1) + (9/10 -1/4)
= 1 + (9/10 -1/4)
= 1 + (18/20 - 5/20)
= 1 13/20 . . . miles left to walk
___
Using a calculator:
5 -2.1 -1.25 = 1.65 = 1 65/100 = 1 13/20
Find the equation of the line that passes through (-2,5) and is parallel toy= -1/3x+2
Answers
If lines are parallel, then their slopes are equal, so m=-1/3.
So we can write
y=(-1/3)x+b
To find be, we need substitute value's of x and y using point (-2,5).
5=(-1/3)*(-2)+b
5=2/3+b
b= 5-2/3=15/3-2/3=13/3
The equation of the line is
y=(-1/3)x+13/3
He altitude of a triangle is increasing at a rate of 3000 centimeters/minute while the area of the triangle is increasing at a rate of 3500 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 10000 centimeters and the area is 89000 square centimeters?
Answers
A = (1/2) * (b) * (h)
Where,
b: base of the triangle
h: height of the triangle
Deriving the area we have:
A '= (1/2) * ((b') * (h) + (b) * (h '))
Clearing b' we have:
b '= (2A' - (b) * (h ')) / (h)
We must look for the value of the base:
A = (1/2) * (b) * (h)
Substituting values:
89000 = (1/2) * (b) * (10000)
b = (89000) / (5000)
b = 17.8 cm
Then, the speed at which the base changes is:
b '= (2 * (3500) - (17.8) * (3000)) / (10000)
b '= -4.64 cm / min
Answer:
The base of the triangle is decreasing at:
4.64 cm / min
Can someone show me how to do this?
16! / 4! 12!
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Lines that are not in the same plane are called _____ lines. A.perpendicular B.transversal C.skew D.parallel
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Skew is a line that does not have a same plane.
Hope it helped you.
-Charlie
Thanks!
Lines that are not in the same plane are called skew lines.
What is a line?"A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely."
Given, two lines are not in the same plane.
Here, perpendicular lines, transversal lines, and parallel lines should be in the same plane.
Two lines are called skew lines are two lines if they do not intersect and are not parallel.
Therefore, skew lines are not in the same plane.
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Anyone know?
A. 99
B. 100
C. 121
D. Cannot be determined
Answers
Since, it is given that the pentagon ABCDE is congruent to pentagon FGHIJ.
By being congruent, the corresponding angles and sides are equal.
Therefore, [tex]\angle A = \angle F[/tex], [tex]\angle B = \angle G[/tex], [tex]\angle C = \angle H[/tex], [tex]\angle D= \angle I[/tex], [tex]\angle E = \angle J[/tex].
By using [tex]\angle A = \angle F[/tex]
So, [tex]100^\circ = \angle 1[/tex]
Therefore, the measure of angle 1 is 100 degrees.
So, Option B is the correct answer.
You are looking at two different houses. house #1 would have a daily 5-mile commute to work, while house #2 would have a daily 20-mile commute. how much more co2 would you produce annually if you buy house #2? (hint: driving 1 mile produces 1.1 lb of co2 and you work 240 days/year.)
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5 (miles a day) x 240 (work days a year) = 1,200 miles
total co2 produced = 1.1 x 1200 = 1,320 lbs of CO2 a year
Annual Commute from house 2:
20 (miles a day) x 240 (work days a year) = 4,800 miles
Total CO2 produced = 1.1 x 4800 = 5,280 lbs of CO2 a year
Difference = 5,280 - 1,320 = 3,960 more if you buy house 2.
Answer:
B: 3960 lb
Step-by-step explanation:
vhslearning
Which of the following is not an example of like terms? A. 2 and –6 B. 2b and –6b C. 2b and 2 D. 2b^2 and 6b^2
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This is because in order have like terms, they have to have the same properties. One of them (2b) has a variable next to it, while the other does not. This makes them not alike.
Hope this helps! :)
The antarctic peninsula is less than 700 miles from what continent
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A spherical ball of wax with a radius of 4 inches is melted and poured into a container shaped like a rectangular prism with a 6 inch x 6 inch base. What is the height of the melted wax in the new shape?
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Volume of the spherical ball = 4/3 π (4)³ = 267.95 in³
Area of a rectangular prism = Length x Width x Height
267.95 = 6 x 6 x Height
Height = 267.95 ÷ 36 = 7.44 in
Answer: 7.44 inch
A 3-lb force acting in the direction of the vector (3,-1) moves an object just over 9 ft from point (0,5) to (6,-2). Find the work done to move the object to the nearest foot-pound
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Answer: The Work done to move the object is [tex]=23.15 \text { foot pounds }[/tex]
Step-by-step explanation:
Given;
Force F=3 [tex]l b s[/tex]
Vectors of F= (3,-1)
Moves object to a distance=9 [tex]f t s[/tex]
Let A and B be the displacements Vectors
A= (0,-5)
B= (6,-2)
To Find:
Work done in foot-pounds
Solution:
Work done [tex]W=F \times D[/tex]
Direction of force vector= (3,-1) (i, j)
=3i-j
Unit of force vector [tex]=\sqrt{3^{2}+\left(-1^{2}\right)}[/tex]
[tex]=\sqrt{9+1}[/tex]
Force vector=(Force/Unit Vector)Direction of force vectors
F=[tex]3 / \sqrt{10} \times(3 i-j)[/tex]
Direction of motion vector= (B-A)
= (6,-2)-(0,-5) x i,j)
=(6-0),(-2-5) x (i, j)
=(6,-7) x (i, j)
=6i-7j
Unit of motion vector [tex]=\sqrt{6^{2}+\left(-7^{2}\right)}[/tex]
[tex]=\sqrt{36+49}[/tex]
[tex]=\sqrt{85}[/tex]
Motion Vector= (Distance moved by the object/Unit motion vector) × (Direction of motion vectors)
[tex]D=9 / \sqrt{85} \times(6 i-7 j)[/tex]
Workdone [tex]W=F \times D[/tex]
[tex]= [3/ \sqrt{10} \times (3i-j)] \times [9/ \sqrt{85} \times (6i-7j)][/tex]
[tex]= [3/ \sqrt{10} \times 9/ \sqrt{85}] \times [(3i-j) \times(6i-7j)][/tex]
[tex]= [3/3.1623 \times 9/9.2195] \times [(3\times6) + ((-1) \times (-7))][/tex]
[tex]= [0.94867 \times 0.97619] \times [18+7][/tex]
[tex]=23.15 \text { foot pounds }[/tex]
Result:
Work done to move an object [tex]=23.15 \text { foot pounds }[/tex]
Answer:
[tex]W = 25.617\,lbf\cdot ft[/tex]
Step-by-step explanation:
The work done to move the object is:
[tex]W = F \cdot s \cdot \cos \alpha[/tex]
The angle of the force with respect to change in the position vector is:
[tex]\alpha = \tan^{-1}\left(-\frac{7}{6} \right) - \tan^{-1}\left(-\frac{1}{3} \right)[/tex]
[tex]\alpha \approx 18.415^{\textdegree}[/tex]
The magnitude of the work done is:
[tex]W = (3\,lbf)\cdot (9\,ft)\cdot \cos 18.415^{\textdegree}[/tex]
[tex]W = 25.617\,lbf\cdot ft[/tex]
please help with this??
Answers
The mode is the number that is repeated more often than any other, so 62 is the mode.
Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q. 3 + x - 3x2 = 9 A) (x - 1 6 )2 = 71 36 B) (x - 1 3 )2 = 71 36 C) (x - 1 6 )2 = - 71 36 Eliminate D) (x - 1 3 )2 = - 71 36
Answers
3+x-3x^2=9
putting like terms together we have:
-3x^2+x=6
dividing through by -3 we get:
x^2-x/3=-2
but
c=(b/2a)^2
c=(-1/6)^2=1/36
thus the expression will be:
x^2-x/3+1/36=-2+1/36
1/36(6x-1)²=-71/36
the answer is:
1/36(6x-1)²=-71/36
Help please??????????
Answers
substitute the value of x:
[tex]|PR|=18\cdot18+14=324+14=338[/tex]
The recursive rule for a sequence is shown. an=an−1+7 a1=17 what is the explicit rule for this sequence?
Answers
an=a(n-1)+7; a1=17
to get the explicit formula we proceed as follows:
common difference=7
a1=17
but the explicit formula for arithmetic sequence is:
an=a+(n-1)d
where:
a=fist term
n=number of terms
d=common difference
plugging the values in the formula we get:
an=17+(n-1)7
simplifying we get
an=17+7n-7
an=7n+10
Answer: an=7n+10
The explicit rule for the sequence is [tex]a_n = 10 + 7n[/tex]
The recursive rule is given as:
[tex]a_n=a_{n-1}+7[/tex]
[tex]a_1 = 17[/tex]
The above shows that the sequence is an arithmetic sequence.
Start by calculating a2
We have:
[tex]a_n=a_{n-1}+7[/tex]
Substitute 2 for n
[tex]a_2=a_1+7[/tex]
This gives
[tex]a_2 = 17 + 7[/tex]
[tex]a_2 = 24[/tex]
So, we have:
a1=17
a2 = 24
The common difference (d) is:
d =a2 - a1
d = 24 - 17
d = 7
The explicit rule is then calculated as:
[tex]a_n = a_1 + (n - 1)d[/tex]
This gives
[tex]a_n = 17 + (n - 1) * 7[/tex]
Expand
[tex]a_n = 17 - 7 + 7n[/tex]
[tex]a_n = 10 + 7n[/tex]
Hence, the explicit rule for the sequence is [tex]a_n = 10 + 7n[/tex]
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What is the answer to the jones family plans a trip to the amusement park...
Answers
This is because all of the costs of the different items will add up depending on how much of them the family buys. This is why they all have the corresponding variables next to the prices. The prices of those items will be added on to the initial cost of the 128$ family package, so all of the prices would be added up together to get the total.
At a high school 7 student volunteer for a committtee how many different 5 person committees can be chosen
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Number of committee = 5
Number of ways of selecting the committee from the 7 volunteers = 7C5 = 7!/(5!*2!) = 21 ways.
There are 21 ways in which the 5-committee member can be selected from the 7 volunteers.
Using the combination formula, 21 different 5-person committees can be chosen from a group of 7 students.
To determine how many different 5-person committees can be chosen from a group of 7 students, we use the concept of combinations, specifically the combination formula which is defined as:
C(n, k) = n! / [k! * (n - k)!]
where n is the total number of items to choose from, k is the number of items to choose, and the exclamation point represents a factorial, which is the product of all positive integers up to that number.
Applying this to the given problem, we have:
C(7, 5) = 7! / [5! * (7 - 5)!]
This simplifies to:
C(7, 5) = (7 * 6) / (2 * 1)
Therefore, C(7, 5) = 21.
There are 21 different 5-person committees that can be formed from 7 students.
Which path is a Hamiltonian circuit?
Answers
Jesse earns $420 a week, and he works 5 days a week. What is his daily wage?
A. $84
B. $415
C. $60
D. $425
Answers
$84 is his daily wage
A die is thrown twice. What is the probability that:
1. Neither a doublet ordered pair nor a total of 10 will appear?
2. Neither a multiple of 2 on the first throw nor a total of 6 will appear?
A. 7/9
B. 5/12
Answers
2.) B would be your answer.
Answer:
1.)- B. 5/12
2)- A. 7/9
Step-by-step explanation:
ind the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2). (answer in slope-intercept form)
Answers
Find the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2)
y - 3x = – 8-----> y=3x-8------> the slope m=3
we know that
if two lines are perpendicular
then
m1*m2=-1
m1=3
so
m2=-1/3
with m=-1/3 and point (3, 2) find the equation of the line
y=mx+b
2=(-1/3)*3+b------> 2=-1+b-----> b=3
the equation of the line is
y=(-1/3)x+3
the answer is
y=(-1/3)x+3
see the attached figure
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3. Use the Fermi process to estimate the number of bricks needed to fill an empty bathtub. Show your work.
My teacher said you can use approximate dimensions of the bricks and bathtub. He said use the easiest ones so that it will be easy to solve.
Answers
brick: 8 x 4 x 2
fermi process:
(60 x 30 x 18) / (8 x 4x 2)
= 32,400 / 64
= 506.25
estimated as 500 bricks