No Alan did not break even
Alan incured a loss of 6.25 %
Solution:
Given that,
Alan bought two bikes
He sold one to Beth for $300 taking a 25% loss
He also sold one to Greta for $300 making a 25% profit
When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss
Which is given as:
[tex]loss\ \% = (\frac{x}{10})^2[/tex]
Here, x = 25
[tex]loss\ \% = (\frac{25}{10})^2\\\\loss\ \% = 2.5^2\\\\loss\ \% = 6.25[/tex]
Thus the loss percentage is 6.25 %
Danica is in the observation area of the sears tower in chicago overlooking lake michigan. She sights two sailboats going due east from the tower. The angles of depression to the two boats are 42 degrees and 29 degrees. If the observation deck is 1,353 feet high, how far apart are the boats?
The distance between the two sailboats is approximately 2,197 feet.
1. Find Distances to Boats:
- Use the tangent function for each angle of depression to find the distances from the observation deck to each sailboat. For boat 1 (42 degrees), use [tex]\(\tan(42^\circ) = \frac{\text{height}}{\text{distance}}\)[/tex], and for boat 2 (29 degrees), use [tex]\(\tan(29^\circ) = \frac{\text{height}}{\text{distance}}\)[/tex].
2. **Calculate Individual Distances:**
- For Boat 1: [tex]\( \text{Distance}_{\text{Boat 1}} = \frac{\text{height}}{\tan(42^\circ)} \)[/tex]
- For Boat 2: [tex]\( \text{Distance}_{\text{Boat 2}} = \frac{\text{height}}{\tan(29^\circ)} \)[/tex]
3. Determine Distance Between Boats:
- The distance between the two boats is [tex]\( \text{Distance}_{\text{Boat 1}} - \text{Distance}_{\text{Boat 2}} \)[/tex].
4. Final Answer:
- The final answer is the distance between the two sailboats, which is approximately 2,197 feet.
What is the sum of 6 and g then g is added to 6
Answer:
12 + 2g ?
Step-by-step explanation:
6 + 6 = 12. g + g = 2g. So together you get 12 + 2g. I am not 100% sure.
3(1)+3(-x/3)=3(5x/3)
Answer:
x= 1/2
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
3(1)+3(-x/3)=3(5x/3)
3-x=5x
3=x+5x
3=6x
x=3/6
simplify
x=1/2
Is y= -3x + 10 a linear function
Answer: yes
Step-by-step explanation:Can you brainless me
-12.11x - 10.5 = 75.6 - 3.5x
Answer:
x = −10
Step-by-step explanation:
1. Add 12.11x to both sides.
−10.5 = 75.6 − 3.5x + 12.11x
2. Simplify 75.6 - 3.5x + 12.11x to 75.6 + 8.61x.
−10.5 = 75.6 + 8.61x
3. Subtract 75.6 from both sides.
−10.5 − 75.6 = 8.61x
4. Simplify −10.5 −75.6 to −86.1.
−86.1 = 8.61x
5. Divide both sides by 8.61.
[tex]-\frac{8.61}{86.1}[/tex] = x
6. Simply [tex]-\frac{8.61}{86.1}[/tex] to 10
−10 = x
7. Flip it.
x = −10
1) In the diagram, l || m. If the measure of angle 3 is 120 find the measure of the following angles
a) angle 4
b) angle 6
c) angle 8
2)Describe the sequence of transformations from quadrilateral WXYZ to W” X” Y” Z”.
Answer:
i) angle 3 is 120°
ii) angle 3 + angle 4 = 180° as both angles make up a staright line
∴ angle 4 = 180° - angle 3 = 180° - 120° = 60°
iii) angle 6 = angle 3 = 120° as they are opposite interior angles
iv) angle 6 + angle 8 = 180° as both angles make up a straight line
∴ angle 8 = 180° - angle 6 = 180° - 120° = 60°
Step-by-step explanation:
i) angle 3 is 120°
ii) angle 3 + angle 4 = 180° as both angles make up a staright line
∴ angle 4 = 180° - angle 3 = 180° - 120° = 60°
iii) angle 6 = angle 3 = 120° as they are opposite interior angles
iv) angle 6 + angle 8 = 180° as both angles make up a straight line
∴ angle 8 = 180° - angle 6 = 180° - 120° = 60°
The slope of (3,6) and (5,2)
[tex]\text{Hey there!}[/tex]
[tex]\mathsf{The\ slope\ formula\ is: \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\mathsf{y_2=2}\\\mathsf{y_1=6}[/tex]
[tex]\mathsf{x_2=5}\\\mathsf{x_1=3}[/tex]
[tex]\mathsf{Equation: \dfrac{2-6}{5-3}}\\\\\bullet\mathsf{2-6=-4\leftarrow your\ \bf{y}\mathsf{\ value}}\\\\\bullet{\mathsf{5-3=2\leftarrow your\ \bf{x}\ \mathsf{value}}}\\\\\mathsf{New\ equation/answer:\ \dfrac{-4}{2}}\\\\\boxed{\bf{Answer:\mathsf{-2\ or\ \dfrac{-4}{2}}}}[/tex]
[tex]\text{Good luck on your assignment enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
.There are 850 Douglas fir and Ponderosa pine trees in a section of forest bought by Karamazov Logging Co. The company paid an average of $300 for each Douglas fir and $225 for each Ponderosa pine. If the company paid $217,500 for the trees, how many of each kind did the company buy
The number of Douglas fir pine trees is 350, and the number of Ponderosa pine trees is 500
Applications of Simultaneous equationFrom the question, we are to determine the number of each kind of pine trees.
Let x represent Douglas fir pine trees
and y represent Ponderosa pine trees
From the first statement - There are 850 Douglas fir and Ponderosa pine trees
We can write that
x + y = 850 ------------- (1)
Also,
The company paid an average of $300 for each Douglas fir and $225 for each Ponderosa pine; and the company paid $217,500 for the trees.
From this statement, we can write that
300x + 225y = 217500 ---------------- (2)
Now, we will solve the equations simultaneously
From equation (1)
x + y = 850
Then,
x = 850 - y ------------ (3)
Substitute this into equation (2)
300x + 225y = 217500
300(850-y) + 225y = 217500
255000 -300y + 225y = 217500
255000 - 75y = 217500
255000 - 217500 = 75y
37500 = 75y
∴ y = 37500/75
y = 500
Substitute the value of y into equation (3)
x = 850 - y
x = 850 - 500
x = 350
∴ x = 350 and y = 500
Hence, the number of Douglas fir pine trees is 350, and the number of Ponderosa pine trees is 500
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What to decimals do you add to get 54.57
Answer:
[tex]Any\ two\ equations\ x,\ 54.57-x\\\\For\ example\ 23.37+31.20=54.57[/tex]
Step-by-step explanation:
[tex]Let\ first\ decimal=x\\\\Second\ decimal=y\\\\x+y=54.57\\\\y=54.57-x\\\\so\ any\ two\ decimal\ x\ and\ 54.57-x\ will\ give\ 54.57\\\\If\ we\ take\ first\ decimal(x)=23.37\\\\second\ decimal=54.57-23.37\\\\second\ decimal=31.20\\\\\Rightarrow 23.37+31.20=54.57[/tex]
If there is a 60% chance of rain tomorrow and a 40% chance of wind and rain,
what is the probability that it is windy, given that it is rainy? Round your
answer to the nearest percent.
O A. 78%
O B. 71%
OC. 67%
O D. 33%
Answer:
67%
Step-by-step explanation:
we are given the probability of rain tomorrow of 60 % and a 40% chance of wind and rain. we are asked for the probability that it is windy, given that it is rainy. The formula that should be used is the quotient of the probability with "and" over the probability of the rain only. Hence, P[W U R ] / P [R] = 0.4 / 0.6 = 2/3 = 67%
:Answer: 67%
Step-by-step explanation:
APEX
Dave works 5 hours at double time. He earns $98.00. Find his normal hourly rate?
Answer:
You just divide the numbers to get the hourly pay.
98÷5÷2
$9.80/hr
what is the equation for 10x + 35
Answer:
5(2x + 7)
Step-by-step explanation:
Let Y represent Jaron’s age in years. If Dawn were 5 years older, she would be Jaron’s age. Which expression represents Dawn’s age?
Answer:5-y=a
Step-by-step explanation:
Which of the following is equivalent to 4x – 3y = -6?
Answer:
Hello, Subtract 4x 4 x from both sides of the equation. Divide each term by 3 3 and simplify. Divide each term in 3y=−4x+15 3 y = - 4 x + 15 by 3 3 . Use the slope-intercept form to find the slope and y-intercept.
Hope This Helps!
Terrence and Lee were selling magazines for a charity. In the first week, Terrance sold 30% more than Lee. In the second week, Terrance sold 12 magazines, but Lee did not sell any. If Terrance sold 50% more than Lee by the end of the second week, how many magazines did Lee sell?
Choose any model to solve the problem. Show your work to justify your answer.
Lee sold 60 magazine
Step-by-step explanation:
Terrence and Lee were selling magazines for a charity
In the first week, Terrance sold 30% more than LeeIn the second week, Terrance sold 12 magazines, but Lee did not sell anyTerrance sold 50% more than Lee by the end of the second weekWe need to find how many magazines Lee sold
Assume that Lee sold x magazines
∵ Terrance sold 30% more than Lee in the first week
∵ Lee sold x magazines in the first week
- Find 30% of x and add it to x to find how many magazines
Terrance sold
∵ Terrance sold = 30% × x + x
∴ Terrance sold = [tex]\frac{30}{100}[/tex] × x + x = 0.3 x + x
∴ Terrance sold = 1.3 x magazines in the first week
∵ Terrance sold 12 magazines in the second week
- Add 1.3 x to 12 to find the number of magazines that Terrence
sold in the two weeks
∴ Terrence sold 1.3 x + 12 magazines in the two weeks
∵ Lee did not sell any in the next week
∴ Lee sold x magazines in the two weeks
∵ Terrance sold 50% more than Lee by the end of the 2nd week
- Equate 1.3 x + 12 by the sum of x and 50% of x
∴ 1.3 x + 12 = 50% × x + x
∵ 50% × x = [tex]\frac{50}{100}[/tex] × x = 0.5 x
∴ 1.3 x + 12 = 0.5 x + x
- Add the like terms in the right hand side
∴ 1.3 x + 12 = 1.5 x
- Subtract 1.3 x from both sides
∴ 12 = 0.2 x
- Divide both sides by 0.2
∴ 60 = x
Lee sold 60 magazine
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8 1/5 + (4 2/5 + 3 3/10
Answer:
15 and 9/10 or 15.9
Step-by-step explanation:
4_2/5 + 3_3/10 = 4_4/10 + 3_3/10 = 7_7/10
8_1/5 = 8_2/10
8_2/10 + 7_7/10 = 15 9/10
or 15.9
Answer:15 and 9 10ths
Step-by-step explanation:
5x + 2y = 8
x
+y=4
If you want to solve the system of equations by addition, which of the following could you do?
Multiply the second equation by 5 and add.
Multiply the second equation by 2 and add.
Multiply the second equation by -2 and add.
NEXTOUESTION
ASK FOR HEID
Answer:
you multiply the second equation by -2.
Step-by-step explanation:
to get rid of y and find x. Then you plug x into one of the equations to find y
Factor the expression:
30 + 100c
Consider circle H with a 3 centimeter radius. If the length of minor arc RS is 5
2
π, what is the measure of ∠RST? Assume that chords RS and TS are congruent.
A) 20°
B) 25°
C) 30°
D) 40°
Answer:
b 25
Step-by-step explanation:
Answer: its c: 30
Step-by-step explanation:
i just got this wrong so haha
Archimedes went to sleep beside a big rock. He wanted to get up at 777 AM, but the alarm clock was yet to be invented! He decided to sleep at the spot where the rock's shadow should end when it's 777 AM so as to be awakened by the direct sunlight.
Archimedes knew that at 777 AM, the sunlight reaches the ground at an angle of 31^\circ31
∘
31, degrees. The rock beside which he slept was 555 meters tall.
How far from the rock did Archimedes go to sleep?
By using the tangent function tan(31°) = opposite/adjacent, and knowing the rock's height of 555 meters, we can find the distance from the rock that Archimedes should sleep to wake up with direct sunlight. The distance is calculated as the height of the rock divided by the tangent of the angle of the sun, which will give the desired result.
Explanation:To find out how far from the rock Archimedes went to sleep, we can use the concept of trigonometry. Specifically, we will use the tangent function, which relates the angle of the sun to the height of the rock and the distance of the shadow on the ground.
Given that the sunshine angle is 31 degrees and the rock is 555 meters tall, we can set up our equation using the tangent function: tan(31°) = opposite/adjacent, where the opposite side is the height of the rock, and the adjacent side is the distance from the rock where Archimedes slept.
The equation would look like this:
tan(31°) = 555 / distance
To solve for the distance, we rearrange the equation:
distance = 555 / tan(31°)
By calculating this, we would get the distance where Archimedes should sleep to be woken by the direct sunlight.
Allen and Beverly thought of the same number. Allen doubled the number and added 15 to the result. He got 51. Beverly performed the same operations with the number, but in reverse order. What did she get?
Allen and Beverly both thought of the number 18. When Allen doubled the number and added 15, he got 51. Beverly, in reverse order, subtracted 15 from the number and then doubled it to get 6.
Let the number that Allen and Beverly thought of be represented by 'x'.
Allen doubled the number and added 15 to the result, which gives us the equation:2x + 15 = 51
Now, we need to solve for 'x' to find the original number.
Subtract 15 from both sides of the equation: 2x = 51 - 15
2x = 36
Now, divide both sides by 2 to isolate 'x': x = 36 / 2
x = 18
So, Allen and Beverly both thought of the number 18.
Now, Beverly performs the same operations but in reverse order: 1. She starts with the number 18.
2. She subtracts 15 from it:18 - 15 = 3
3. Then, she doubles the result:2 * 3 = 6
So, Beverly gets the result of 6 by performing the same operations in reverse order.
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tina is a waitress that makes $10.40, but an average 8 hour shift for her brings in an additional $85 in tips. how much does tina make per hour as a waitress
Answer:
Tina makes per hours [tex]=\$11.925[/tex]
Step-by-step explanation:
Tina makes [tex]8[/tex] hours [tex]=\$10.40[/tex]
and additional tips [tex]=\$85[/tex]
total amount makes for [tex]8[/tex] hours [tex]= \$10.40+\$85[/tex]
total amount makes for [tex]8[/tex] hours [tex]=\$95.40[/tex]
total amount makes for [tex]1[/tex] hours [tex]=\frac{total\ amount}{total\ time}\\\\=\frac{\$95.40}{8}\\\\=\$11.925[/tex]
I can't get the answer!!!! >:(
Answer:
The scale factor of the smaller rectangle to the larger rectangle is 3/2
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
In this problem
To find out the scale factor of the smaller rectangle to the larger rectangle. set up a proportion
[tex]\frac{9}{6}=\frac{3}{2}[/tex] ----> ratio of corresponding heights
or
[tex]\frac{12}{8}=\frac{3}{2}[/tex] ----> ratio of corresponding bases
therefore
The scale factor of the smaller rectangle to the larger rectangle is 3/2
What is the value of 1/6^0?
1/6
0
1
undefined
Answer:
1
Step-by-step explanation:
Simplify the following:
(1/6)^0
Hint: | Any nonzero number to the zero power is one.
(1/6)^0 = 1:
Answer: 1
Many of the colors in them were 'home dyed" although commercial dyes were unknown.
Read the passage. Look at the underlined section marked number 5. There may be a mistake in the way the sentence is written. If you
find a mistake, choose the answer that corrects the mistake. If there is no mistake, choose 'Correct as is.'
es )))
Correct as is
Many of the colors in them were 'home dyed, as commercial dyes were
unknown
Many of the colors in them were 'home dyed if commercial dyes were
unknown
Many of the colors in them were 'home dyed' whereas commercial dyes
were unknown
Answer:
b
Step-by-step explanation: i just know
Answer:
bb
Step-by-step explanation:
Many of the colors in them were "home dyed," as commercial dyes were unknown is the correct answer because "As" correctly begins the subordinate clause and shows the relationship to the main clause
12 one half times one nine
Answer:
[tex]1\frac{7}{18}[/tex] or one seven eighteenths
Step-by-step explanation:
we know that
12 one half times one nine is the same that multiply 12 one half by one nine
so
[tex](12\frac{1}{2})(\frac{1}{9})[/tex]
Convert mixed number to an improper fraction
[tex]12\frac{1}{2}=12+\frac{1}{2}=\frac{12*2+1}{2}=\frac{25}{2}[/tex]
substitute
[tex](\frac{25}{2})(\frac{1}{9})=\frac{25}{18}[/tex]
Convert to mixed number
[tex]\frac{25}{18}=\frac{18}{18}+\frac{7}{18}=1\frac{7}{18}[/tex]
therefore
12 one half times one nine is one seven eighteenths
A ladder on a fire truck has its base 8 ft. above the ground. The maximum length of the ladder is 100 feet. If the greatest acute angle the ladder can make with the ground is 70°, what is the highest it can reach?
Answer:
78 degrees
Step-by-step explanation:
It’s already above the grown by 8 feet 100 feet in the air but can only go 70
Which expression is equivalent to 1/3y
Answer:
1/6y + 1/6(y + 12) - 2
Answer:
C
Step-by-step explanation:
Edge 2020
what is cos 0 if sec 0=2?
Step-by-step explanation:
[tex] \because \: \cos \theta = \frac{1}{\sec \theta} \\ \\ \therefore \: \cos \theta = \frac{1}{2} \\ \\ \therefore \: \cos \theta = \cos 60 \degree \\ \\ \huge \red{ \boxed{\therefore \: \theta = 60 \degree}}[/tex]
Answer:1/2
Step-by-step explanation:Plato
[x^(-2)]^2 how do you simplify
Answer:
[tex](x^2)^2=x^4[/tex]
Step-by-step explanation:
Because of the power of a power property states that [tex]((x^n)^m)=x^{n\times{m}}[/tex], where n and m are real numbers, then, the expression you have just posted can be simplified by applying this property to [tex](x^2)^2=x^{2\times2}=x^4[/tex].