Answer:
Gas Cost Per Month: Car A $21.43, Car B $31.58
Insurance Cost Per Month: Car A $125, Car B $83.33
Maintenance Cost Per Month: Car A $25, Car B $41.67
Total Cost Per Month: Car A $171.43, Car B $156.58
Step-by-step explanation:
Gas Cost Per Month:
It is a 20 mile round trip per day, so five days a week would be 100 miles. This means that you drive 400 miles to work in one month. So for Car A, 400/28 = 14.29 gallons. 14.29 gallons times $1.50 = $21.43 per month. For Car B, 400/19 = 21.05 gallons. 21.05 Gallons times $1.50 = $31.58 per month.
Insurance Cost Per Month:
Car A costs $1,500 to insure for one year. So if we take 1,500 and divide it by 12 we get $125 per month. Car B costs $1,000 to insure for one year. So taking 1,000 and dividing by 12 gives us roughly $83.33.
Maintenance Cost Per Month:
Car A costs $300 per year, so taking 300 and dividing by 12 gives us $25 per month. Car B costs $500 per year, so taking 500 and dividing by 12 gives us roughly $41.67 per month.
Total Cost Per Month:
Now all we need to do is add everything together. For Car A, we have $21.43 in gas, $125 in insurance, and $25 in maintenance. This gives a grand total of $171.43 per month. For Car B, we have $31.58 in gas, $83.33 in insurance, and $41.67 in maintenance, leaving a grand total of $156.58.
Hope this helps!
To compare the monthly operating costs of Car A and Car B, calculate and sum up the gas, insurance, and maintenance costs for each car. Car B, with a total monthly cost of $156.58, is less expensive to operate than Car A, which costs $171.43 per month.
To compare the cost of operating two different vehicles for one month, we need to calculate the monthly gas, insurance, and maintenance costs for each vehicle and then add them up to get the total monthly cost.
Calculating Costs for Car A
Gas Cost per Month: You drive 20 miles a day for 5 days a week, that's 100 miles a week or 400 miles for 4 weeks (1 month). At 28 miles per gallon, you would need roughly 14.29 gallons (400/28) per month. At $1.50 per gallon, the monthly gas cost is 14.29 gallons * $1.50/gallon = $21.43.Insurance Cost per Month: $1,500 per year translates to $125 per month ($1,500/12 months).Maintenance Cost per Month: $300 a year equates to $25 per month ($300/12 months).Total Cost for Car A per Month = Gas + Insurance + Maintenance = $21.43 + $125 + $25 = $171.43.Calculating Costs for Car B
Gas Cost per Month: With the same driving pattern, you would need roughly 21.05 gallons (400/19) per month. At $1.50 per gallon, the monthly gas cost is 21.05 gallons * $1.50/gallon = $31.58.Insurance Cost per Month: $1,000 per year is about $83.33 per month ($1,000/12 months).Maintenance Cost per Month: $500 a year is about $41.67 per month ($500/12 months).Total Cost for Car B per Month = Gas + Insurance + Maintenance = $31.58 + $83.33 + $41.67 = $156.58.Comparing the total monthly costs, Car B is less expensive to operate than Car A.
Carrie made 127 brownies and packed 13 in each box. How many boxes are
packed and how many brownies are left over?
9 boxes and brownies left over
Answer:
9 boxes are packed and 10 brownies are left over.
Step-by-step explanation:
Carrie made 127 brownies and packed 13 in each box.
The number of boxes packed are; [tex]\frac{127}{13}[/tex] = 9[tex]\frac{10}{13}[/tex]
Which means that 9 boxes were packed and 10 brownies were left over.
find the equation of a line in point slope form with a slope of 3 going through the point (4,-6)?
Answer:
Equation of line: y=3x-18
Step-by-step explanation:
Point: (4,-6) and slope = 3
[tex]y+6=3(x-4)[/tex]
y=3x-18
Answer:
y + 6 = 3(x - 4)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = 3 and (a, b) = (4, - 6), hence
y - (- 6) = 3(x - 4), that is
y + 6 = 3(x - 4) ← in point- slope form
The equation tan(x- pi/3) is equal to _____.
Answer:
D
Step-by-step explanation:
we can use the formula of tan(A-B) to solve this equation .
The formula is
[tex]tan(A-B)= \frac{tanA-tanB}{1+tanA.tanB}[/tex]
In our question , A is x and B is [tex]\frac{\pi }{3}[/tex]
so when we apply these in the question we get
[tex]tan(x-\frac{\pi }{3} )=\frac{tanx-tan\frac{\pi }{3} }{1+tanx.tan\frac{\pi }{3} }[/tex]
Now since [tex]tan\frac{\pi }{3} = \sqrt{3}[/tex]
we get
[tex]tan(x-\frac{\pi }{3} )=\frac{tanx-\sqrt{3} }{1+\sqrt{3} tanx.} }[/tex]
so correct option is
D
Use the law of sines to find the value of a.
Law of sines:
What is the best approximation of the value of a?
2.4 cm
2.7 cm
3.0 cm
3.3 cm
Answer:
3.0 cm
Step-by-step explanation:
The Law of Sines states the relationship between the sides and the angles of non-right (oblique) triangles.
In the given triangle,the following relation holds;
[tex]\frac{4.7}{sin(95)}=\frac{a}{sin(40)}\\\\a=\frac{4.7}{sin(95)}*sin(40)\\\\a=3.03[/tex]
Answer:
Option C. a = 3.0 cm
Step-by-step explanation:
We have to find the value of a from the given triangle ABC.
By applying sine rule in ΔABC
[tex]\frac{sin95}{4.7}=\frac{sin40}{a}[/tex]
Now we cross multiply in the given equation.
a(sin95°) = 4.7(sin40°)
a(0.9962) = 4.7(0.6428)
a = [tex]\frac{4.7(0.6428)}{0.9962}[/tex]
a = 3.03 cm ≈ 3.0 cm
Therefore, a = 3.0cm Option C. will be the answer.
factorise 21x^2-14y^2
Answer:
[tex]\large\boxed{21x^4-14y^2=7(3x^4-2y^2)=7(x^2\sqrt3-y\sqrt2)(x^2\sqrt3+y\sqrt2)}[/tex]
Step-by-step explanation:
[tex]21x^4-14y^2=7(3x^4-2y^2)\\\\=7\bigg((\sqrt3)^2x^{2\cdot2}-(\sqrt2)^2y^2\bigg)\qquad\text{use}\ (a^n)^m=a^{nm}\ \text{and}\ (ab)^n=a^nb^n\\\\=7\bigg((x^2\sqrt3)^2-(y\sqrt2)^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=7(x^2\sqrt3-y\sqrt2)(x^2\sqrt3+y\sqrt2)[/tex]
Divide in simplest form
Well, you can’t really divide a fraction because it is already a division problem. So we have to do the opposite.
9/4 divided by3/16
Leave the first fraction alone
Change the division sign into a multiplication sign.
Then switch the denominator and numerator of the second fraction, this new fraction is called a reciprocal.
Now multiply the numerators together and the denominators together and simplify.
You get: 144/12
Simplified the answer is : 12
Shawna and her best friend Keisha go shopping. The function p(t) = 3x +2x-4x2+ 21 represents how much money each girl spent based on the number of hours they were shopping. If Shawna and Keisha each go shopping for 2 hours, how much money did they spend together?
Answer:
[tex]\$30[/tex]
Step-by-step explanation:
we have
[tex]p(t)=3x+2x-4x^{2}+21[/tex]
Find the amount of money that each girl spent
For t= 2 hours
[tex]p(2)=3(2)+2(2)-4(2)^{2}+21[/tex]
[tex]p(2)=10-16+21[/tex]
[tex]p(2)=\$15[/tex]
Find the amount of money that they spend together
Multiply by 2 the amount of money that each girl spent
[tex](2)\$15=\$30[/tex]
Shawna and Keisha spent $30 together when each of them went shopping for 2 hours.
It seems there might be a typo in the function p(t) you provided. It should be[tex]\( p(t) = 3t + 2t - 4t^2 + 21 \)[/tex], where t represents the number of hours spent shopping.
To find out how much money Shawna and Keisha spent together when each of them went shopping for 2 hours, we need to evaluate the function p(t) at [tex]\( t = 2 \)[/tex] and then add the results.
Let's plug in t=2 into the function p(t):
[tex]\[ p(2) = 3(2) + 2(2) - 4(2)^2 + 21 \][/tex]
[tex]\[ = 6 + 4 - 16 + 21 \][/tex]
[tex]\[ = 10 - 16 + 21 \][/tex]
[tex]\[ = 15 \][/tex]
Multiply by 2 since $15 is for each girl = 2*$15= $30
Please help me out!!!
Answer:
8
Step-by-step explanation:
Use the Pythagorean theorem.
a^2 + 6^2 = 10^2
a^2 + 36 = 100
a^2 = 64
a = 8
what is the value of x in this figure?
Answer:
D
Step-by-step explanation:
In a 30-60-90 triangle, if the short leg is x, then the long leg is x√3, and the hypotenuse is 2x.
Here, the hypotenuse is 10. So the short leg is:
10 = 2x
x = 5
If the short leg is 5, then the long leg is 5√3.
convert 7.2•10•-3 to standard form
Answer:
0.0072
Step-by-step explanation:
7.2 x [tex]10^{-3}[/tex]
=7.2 x 0.001
=0.0072
Answer:
0.0072
Step-by-step explanation:
The given expression is as follows:
7.2 * 10^(-3)
This expression is in scientific notation, We need to convert it to standard notation for which we will convert the power of 10 to 0.
The power of 10 here is -3. So we will move the decimal point 3 places to the left and get:
= 0.0072 x 10^0
= 0.0072 x 1
= 0.0072
A cylinder has a base diameter of 16 inches and a height of 18inches. What is the volume in cubic inches, of the nearest tenths place ?
Answer:
3619.11 cubic inches
Step-by-step explanation:
volume of a cylinder is [tex]V=\pi r^2h[/tex]
diameter is 16 in, so radius (r) is 8 in
plug in values: [tex]V=\pi 8^2(18) = 3619.11[/tex] cubic inches
The volume of a cylinder with a diameter of 16 inches and a height of 18 inches is calculated using the formula V = πr²h, which results in approximately 3617.3 cubic inches when rounded to the nearest tenths place.
To calculate the volume of a cylinder, we use the formula V = πr²h. Given that the diameter of the cylinder is 16 inches, which means its radius (r) is half of that, 8 inches. The height (h) of the cylinder is given as 18 inches. To find the volume, first square the radius, then multiply by π (approximated as 3.14 for this purpose), and then by the height.
So, the calculation looks like this:
Therefore, the volume of the cylinder, rounded to the nearest tenth place, is 3617.3 cubic inches.
In the first term, 5 is a . In the second term, (3y + 13) is a . In the third term, -1 is a .
The complete statements of the expression are
In the first term, 5 is a coefficientIn the second term, (3y+ 13) is a factorIn the third term, -1 is a constantHow to complete the statements in the expression
From the question, we have the following parameters that can be used in our computation:
5x - 8(3y + 13) - 1
Consider an expression
Ax + b
Where x is the variable, we have
A is a coefficientA is a factorb is a constantUsing the above as a guide, we have the following:
In the first term, 5 is a coefficient
In the second term, (3y+ 13) is a factor
In the third term, -1 is a constant
Question
Use the given expression to complete the statements.
5x– 8(3y + 13) – 1
In the first term, 5 is a _____
In the second term, (3y+ 13) is a ______
In the third term, -1 is a ______
How to solve for y and simplify
-3y = -6/5
-3y(5) = (-6/5)(5)
-15y = -6
y = -6/-15
y = 6/15
y = 2/5
Solve angle ABC by using the measurements angle ABC = 90°, angle BAC = 40°, and a = 10. Round measures of sides to the
nearest tenth and measures of angles to the nearest degree.
Answer:
∠ACB==50°
b=15.6 units
c=11.9 units
Step-by-step explanation:
step 1
Find the measure of angle BCA
we know that
The sum of the interior angles of a triangle must be equal to 180 degrees
∠ABC+∠BAC+∠ACB=180°
substitute the given values
90°+40°+∠ACB=180°
∠ACB=180°-130°=50°
step 2
Find the measure of side b
Applying the law of sines
a/sin(∠BAC)=b/sin(∠ABC)
substitute the given values
10/sin(40°)=b/sin(90°)
b=10/sin(40°)
b=15.6 units
step 3
Find the measure of side c
Applying the law of sines
c/sin(∠ACB)=a/sin(∠BAC)
substitute the given values
c/sin(50°)=10/sin(40°)
c=[10/sin(40°)]*sin(50°)
c=11.9 units
ANSWER:
C=11.9
ABC=90 deg.
BAC=40 deg.
A=10
42 base X + 53 base X = 125 base X
[tex]42_x+53_x=125_x\\4\cdot x^1+2\cdot x^0+5\cdot x^1+3\cdot x^0=1\cdot x^2+2\cdot x^1+5\cdot x^0\\4x+2+5x+3=x^2+2x+5\\x^2-7x=0\\x(x-7)=0\\x=0 \vee x=7[/tex]
There is no numeral system with base 0, so [tex]x=7[/tex].
Consider a triangle ABC like the one below. Suppose that A = 27°, C = 78°, and b = 66. (The figure is not drawn to scale.) Solve
the triangle.
Round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
We don't get to see the figure but we don't need it.
The remaining angle B is
B = 180 - 27 - 78 = 75°
The Law of Sines gives the remaining sides
[tex]\dfrac{a}{\sin A} =\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]a = \dfrac{b \sin A}{\sin B} = \dfrac{66 \sin 27}{sin 75} \approx 31.0203[/tex]
[tex]c = \dfrac{b \sin C}{\sin B} = \dfrac{66 \sin 78}{sin 75} \approx 66.8350[/tex]
Answer: B=75°, a=31.0, c=66.8
No need for "or" on this one. That happens when we know the sine of an angle so there are two possibilities for the angle, an acute one and an obtuse one that's supplementary.
582.5 divided by 2.5
Answer:
You'll get your answer as : 233
The sum of two angles measures is 95 degrees. Angle 2 is 40 degrees smaller than 2 times angle 1. What are the measures of the two angles in degrees?
Answer:
<1 = 45
<2 = 50
Step-by-step explanation:
Let <1 = x
Let <2 = y
=============
x + y = 95
y = 2*x - 40
=============
I think the easiest way to do this is to substitute the second or bottom equation into the top equation. Substitute for y
x + 2x - 40 = 95 Combine like terms on the left.
3x - 40 = 95 Add 40 to both sides.
3x -40+40 = 95+40 Combine
3x = 135 Divide by 3
x = 45
=================
Now use the top equation to solve for y
x + y = 95
45 + y = 95 Subtract 45 from both sides.
45 - 45 + y = 95 -45 Combine
y = 50
Which expression is equivalent to (2 1/2 * 2 3/2)2 ?
For this case we must find an expression equivalent to:
[tex](2 \frac {1} {2} * 2 \frac {3} {2}) ^ 2[/tex]
So, we have:
[tex]2 \frac {1} {2} = \frac {2 * 2 + 1} {2} = \frac {5} {2}\\2 \frac {3} {2} = \frac {2 * 2 + 3} {2} = \frac {7} {2}[/tex]
Rewriting the expression:
[tex](\frac {5} {2} * \frac {7} {2}) ^ 2 =\\(\frac {35} {4}) ^ 2 =\\\frac {35} {4} * \frac {35} {4} =\\\frac {1225} {16} =\\76 \frac {9} {16}[/tex]
Answer:
[tex]76 \frac {9} {16}[/tex]
what is the period of the function y=2sinx?
Answer:
C. 2π
Step-by-step explanation:
Given a wave of the equation y= a sin bx where a and b are constants, then the amplitude is a while the period is 360°/b.
360°= 2π radians
For the provided function, the value of b =
Thus period = 2π/1
=2π radians
Answer: 2 Pi
Step-by-step explanation:
Gary is selling paperback and hardcover books at a yard
sale. He charges $2 for each paperback. He earned $10
in sales of hardcover books. He earned $20 selling books
at the yard sale. How many paperbacks did he sell?
Answer:
Gary sold 5 paperback books
Step-by-step explanation:
each book is equal to $2 and $10 were made in Hardcover
So that only leaves us with ten unaccounted dollars
5x=10
Each book or (x) in this case is two dollars
so it will come out to be five books
A triangle has two congruent sides that measure 8.7 cm and 12.3 cm. Which could be the measure of the third side
Answer:
Option C. 15 cm
Step-by-step explanation:
The correct question is
A triangle has two sides that measure 8.7 cm and 12.3 cm. Which could be the measure of the third side?
A. 2.6 cm
B. 3.6 cm
C. 15 cm
D. 21 cm
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Analyze two cases
Let
x ----> the length of the third side
First case
x+8.7 > 12.3
x>12.3-8.7
x> 3.6 cm
Second case
12.3+8.7 > x
21 > x
Rewrite
x < 21 cm
Use the properties of exponents to rewrite the expression.
(-3yz)(-3yz)(-3yz)(-3yz)
Answer:
Answer is 81y^4z^4
Step-by-step explanation:
The expression is (-3yz) (-3yz) (-3yz) (-3yz).
Since all the four terms have power 1:
(-3yz)^1 (-3yz)^1 (-3yz)^1 (-3yz)^1
We know that we can add the powers if the terms have same base
So,
=(-3yz)^1+1+1+1
=(-3yz)^4
=(-3)^4(y)^4(z)^4.
If the power is an even number than the negative sign changes into positive sign.
=3^4y^4z^4
=81y^4z^4
Thus the answer is 81y^4z^4....
g(x) = x3 + 6x2 + 12x + 8
Determine the function’s value when x = −1.
Answer:
g(-1) = 1
Step-by-step explanation:
Synthetic division is by far the fastest way to evaluate this function at x = -1. Set up synth. div. as follows:
-1 ) 1 6 12 8
-1 -5 -7
----------------------
1 5 7 1
since the remainder is 1, g(-1) = 1
Write 6.92 x 10-8 in standard notation
Answer:
0.0000000692
Step-by-step explanation:
We are given the following number in scientific notation and we are to express it in standard notation:
[tex] 6 . 9 2 \times 1 0 ^ - 8 [/tex]
We know that:
[tex] 6 . 9 2 \times 1 0 ^ { - 8 } = \frac { 6 . 9 2 } { 1 0 ^ { 8 } } = \frac { 6 . 9 2 } { 1 0 0 , 0 0 0, 0 0 0 } = 0 . 0 0 0 0 0 0 0 6 9 2 [/tex]
Therefore, the answer in standard notation is 0.0000000692.
Answer:
0.0000000692
Step-by-step explanation:
6.92 x [tex]10^{-8}[/tex]
= 6.92 x 0.00000001
= 0.0000000692
4 to the second power divided by (3 + 1)
Answer:
4
Step-by-step explanation:
3 + 1 = 4
4 to the second power / 4 is 4
Hello There!
[tex]4^{2}[/tex] is multiplying 4 by itself twice, so we would get an answer of 16.
Finally, we divide 16 by 4 because 3+1=4 and when we do this, we get a quotient of 4
Your Answer Is 4
A company manufactures its product at a cost of $0.50 per item and sells it for $0.85 per item daily overhead is $600 how many items must be manufactured each day in order for the company to break even
so the company has an overhead of $600, usually that involves premises leasing and industrial equipment for the manufacturing of the product, that's cost. The cost to make each item is 50 cents, so if the company produces "x" items, their cost is 0.5x total.
so our cost equation C(x) = 0.5x + 600 <---- items' cost plus overhead.
the company sells the product for 85 cents, so if they sell "x" items, their total revenue or income will be 0.85x.
so our revenue equation is simply R(x) = 0.85x.
as you already know, the break-even point is when.... well, you break even, no losses but no gains either, how much you take in is the same amount that you shelled out, namely R(x) = C(x).
[tex]\bf \stackrel{R(x)}{0.85x}=\stackrel{C(x)}{0.5x+600}\implies 0.35x=600\implies x=\cfrac{600}{0.35} \\\\\\ x\approx 1714.285714285714\implies \stackrel{\textit{rounded up}}{x=1714}[/tex]
Ted weighs twice as much as Julie. Mike weighs three times as much as Julie. Together, Ted, Mike, and Julie weigh 210 lbs. What is the weight of each person?
Julie weighs ___ a0 pounds, Ted weighs ___ a1 pounds, and Mike weighs ___ a2 pounds.
The answer to this question is that Julie weighs 210lbs, Ted weighs 420 (210 multiplied by 2 is 420). Mike weighs 630 (210 multiplied by 3 is 630). So, it would be "Julie weighs 210a0 pounds, Ted weighs 420 a1 pounds, and Mike weighs 630a2 pounds."
I hope this answer helps!
"Stay Brainly and stay proud!" - Zalgo
Answer:
Julie=35 lbs, Ted= 70 lbs, and Mike=105 lbs
Step-by-step explanation:
Julie=x ted=2x mike=3x
The sum of their weight all together is 210 pounds
Combine the x's
6x=210
Divide both sides by 6 to get 1x (Julies weight)
6x/6 = 210/6
1x= 35 (Julie weighs 35 lbs)
35 x 2= 70 ( Ted weighs 70 lbs)
35 x 3= 105 ( Mike weighs 105 lbs)
- Hope this helps!
Which steps will verify that is a rectangle
Answer:
1) Are there 4 right angles? (90° angles)
2) Are there 2 sets of parallel lines?
3) Are there 2 sets of congruent lines?
4) Are there a set of congruent diagonals?
~
Can you help me with this question please? I will reward 20 points for best answer.
* You don't have to solve the problem for me, I just want to know the formula and how to solve it.
"When the fundraiser began, 600 people wanted to purchase the dance troupe’s T-shirts at $12 per T-shirt, but as the group increased the price of their T-shirts, they noticed a fall in the demand. For every $1 increase in price, the demand fell by 50 shirts. The dance troupe’s initial supply was short by 210 T-shirts which corresponded to an initial price of $9.75. For every $1 increase in price, they ordered 40 more T-shirts. Write a system of linear equations to represent both the demand and supply for the T-shirts. Let q represent the quantity of T-shirts and p represent the price."
Answer:
Demand: q = -50p + 1200
Supply: q = 40p
Step-by-step explanation:
First let's define our variables.
q = quantity of T-shirts
p = price
We know that when p = 12, q = 600. When p increases by 1, q decreases by 50. So this is a line with slope -50 that passes through the point (12, 600). Using point-slope form to write the equation:
q - 600 = -50 (p - 12)
Converting to slope-intercept form:
q - 600 = -50p + 600
q = -50p + 1200
Similarly, we know that when p = 9.75, q = 600 - 210 = 390. When p increases by 1, q increases by 40. So this is a line with slope 40 that passes through the point (9.75, 390). Using point-slope form to write the equation:
q - 390 = 40 (p - 9.75)
Converting to slope-intercept form:
q - 390 = 40p - 390
q = 40p