Answer:
$6
Step-by-step explanation:
Susan can easily figure the tip by the following procedure. 10% of the bill is the amount with the decimal point moved one place to the left, so is $4.00. 5% of the bill is half that, or $2.00.
15% of the bill is 10% + 5%, so is $4.00 +2.00 = $6.00. The tip will be $6.00.
*trigonometry and area.*
Find the area of a regular octagon with a side length of 8cm. Round to the nearest tenth.
Answer:
The correct answer is that the area of the regular octagon is 309 cm²
Step-by-step explanation:
There are several formulas for calculating the area of a regular octagon. We will use this one for solving this question because it does not require additional information .
Area = (2 * s²)/tan 22,5°
s = 8 cm
Replacing with the real values, we have:
Area = (2 * 8²)/tan 22,5°
Area = 2 * 64/0.4142
Area = 128/0.4142
Area = 309 cm² (Rounding to the nearest tenth)
Which correlation coefficient best represents a moderate relationship showing fewer anxiety symptoms in people who report higher life satisfaction? –0.5 +0.7 –0.2 +0.4
Answer:
-0.5
Step-by-step explanation:
The correlation coefficient represents the relationship between two variables and here two variables are anxiety symptoms and life satisfaction. As it is mentioned in the statement that less anxiety symptoms are present in the individuals who have higher life satisfaction, so there is negative/ inverse relationship between anxiety symptoms and life satisfaction. Just to be clear the inverse relationship means that increase in one variable lead to decrease in second variable and vice versa. Also according to rule of thumb 0.5 represents the moderation correlation because correlation coefficient ranges from -1 to +1 and 0.5 is a middle value. So the correlation coefficient in the given scenario is -0.5.
An architecture firm creates blueprints for office buildings. Last week, they produced four rectangular blueprints for four different projects. Project A: A 20-inch by 15-inch blueprint with a scale of 1 inch to 4 feet and a projected cost of $22,000. Project B: A 10-inch by 8-inch blueprint with a scale of 1 inch to 8 feet and a projected cost of $25,000. Project C: A 15-inch by 12-inch blueprint with a scale of 1 inch to 6 feet and a projected cost of $27,000. Project D: An 8-inch by 6-inch blueprint with a scale of 1 inch to 12 feet and a projected cost of $30,000. Order the projects from greatest to least projected cost per square foot of the actual offices. Project C Project B Project D Project A
Answer:
Cost in decreasing order: Project B>Project A>Project D>Project C
Step-by-step explanation:
Project A
Area: [tex]A=20 in*15 in= 300 in^2[/tex]
Scale: [tex]S=\frac{4 ft *4ft}{1 in*1in}=16 \frac{ft^2}{in^2}[/tex]
Cost:
[tex]C=\frac{22000}{300 in^2*16 \frac{ft^2}{in^2}}[/tex]
[tex]C=\frac{4.58}{ft^2}[/tex]
Project B
Area: [tex]A=10 in*8 in= 80 in^2[/tex]
Scale: [tex]S=\frac{8 ft *8ft}{1 in*1in}=64 \frac{ft^2}{in^2}[/tex]
Cost:
[tex]C=\frac{25000}{80 in^2*64 \frac{ft^2}{in^2}}[/tex]
[tex]C=\frac{4.88}{ft^2}[/tex]
Project C
Area: [tex]A=15 in*12 in= 180 in^2[/tex]
Scale: [tex]S=\frac{6 ft *6ft}{1 in*1in}=36 \frac{ft^2}{in^2}[/tex]
Cost:
[tex]C=\frac{27000}{180 in^2*36 \frac{ft^2}{in^2}}[/tex]
[tex]C=\frac{4.16}{ft^2}[/tex]
Project D
Area: [tex]A=8 in*6 in=48 in^2[/tex]
Scale: [tex]S=\frac{12 ft *12ft}{1 in*1in}=144 \frac{ft^2}{in^2}[/tex]
Cost:
[tex]C=\frac{30000}{48 in^2*144 \frac{ft^2}{in^2}}[/tex]
[tex]C=\frac{4.34}{ft^2}[/tex]
Cindy's puppy, Zoey, has a basket of toys. There are 3 balls in the basket. There are 2 times as many stuffed animals as balls in the basket. There is 1 fewer bone than stuffed animals. How many toys are in Zoey's basket?
There are 14 toys in Zoey's basket.
Step-by-step explanation:
Given,
Balls in basket = 3
Stuffed animals = 2 times as balls in basket
Stuffed animals = 2*3 = 6
Bones = 1 fewer than stuffed animals.
Fewer means subtraction
Bones = 6-1 = 5
Total toys = Balls + stuffed animals + bones
Total toys= 3+6+5 = 14
There are 14 toys in Zoey's basket.
Keywords: addition, multiplication
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To estimate the length of the lake, caleb starts at one end of the lake and walk 95m. He then turns a 60° angle and walks on a new path and walks 8m more then arrives at the other end of the lake. Approximately how long is the lake?
Answer:
Length of the lake is 97.30 m
Step-by-step explanation:
We have given Caleb starts at one end of the lake and walk 95 m
So [tex]d_1=95m[/tex]
And then he turns at an angle of 60°
So [tex]\Theta =60^{\circ}[/tex] and then again walk 8 m
So [tex]d_2=8m[/tex]
We have to fond the total length of the lake , that is d
Total length of the lake is given by [tex]d=\sqrt{d_1^2+d_2^2+2d_1d_2cos\Theta }=\sqrt{95^2+8^2+2\times 95\times 8\times cos60^{\circ}}=97.30m[/tex]
So length of the lake is 97.30 m
Final answer:
Using the Law of Cosines with Caleb's path measurements of 95 meters and 103 meters at a 60-degree angle, the length of the lake is found to be approximately 104 meters.
Explanation:
To estimate the length of the lake, we can represent Caleb's path as a triangle, where the length of the lake forms one side of the triangle. Caleb starts by walking 95 meters along one side, then makes a 60° angle and walks 8 meters more than the length of the first path, forming the second side of the triangle. The length of the lake, which is the final side, can be calculated using the Law of Cosines.
The Law of Cosines is given by c² = a² + b² - 2ab×cos(γ), where γ is the enclosed angle and a, b, and c are the lengths of the sides of the triangle.
In this case, a = 95m, b = 95m + 8m = 103m, and γ = 60°. Plugging these values into the Law of Cosines, we will find the length of the lake (c).
c² = 95² + 103² - 2×95×103×cos(60°)
c² = 9025 + 10609 - 19570×0.5
c² = 9025 + 10609 - 9785
c² = 10849
c ≈ √10849
c ≈ 104.16 meters
Therefore, the length of the lake is approximately 104 meters long.
A local pizza shop has a membership program for frequent buyers. The membership costs $5 per month and members get a discounted price of $1.50 per slice of pizza. Evan purchased a membership to this pizza shop. How much would Evan have to pay the pizza shop if he bought 7 slices of pizza this month? What would be the monthly cost for x x slices of pizza? Monthly cost for 7 slices: Monthly cost for x x slices:
Evan would have to pay $10.50 to the pizza shop if he bought 7 slices of pizza. The monthly cost for x slices of pizza would be $1.50x.
Explanation:Evan purchased a membership to a pizza shop that has a membership program for frequent buyers. The membership costs $5 per month and members get a discounted price of $1.50 per slice of pizza. If Evan bought 7 slices of pizza this month, he would have to pay $1.50 per slice, since he is a member. Therefore, Evan would have to pay 7 x $1.50 = $10.50 to the pizza shop.
The monthly cost for x slices of pizza can be calculated by multiplying the cost per slice ($1.50) by the number of slices (x). So, the monthly cost for x slices would be x x $1.50 = $1.50x.
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The height of a curved support can be modeled by
f(x) = x^2/256 + 16
Find the width of the beam
Answer:
128
Step-by-step explanation:
I assume there's a negative sign missing, since the image is a downwards parabola.
f(x) = -x²/256 + 16
The width of the beam is the distance between the x-intercepts.
0 = -x²/256 + 16
x²/256 = 16
x² = 4096
x = ±64
So the width is:
64 − (-64) = 128
Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and a two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15.If a customer rolls the dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total amount paid for these second movies will exceed $15.00?
a. 0.91
b. 0.09
c. 0.14
d. 0.86
To find the approximate probability that the total amount paid for the second movies will exceed $15.00 is (a) 0.91, we need to use the expected value and standard deviation to calculate a z-score and then find the corresponding probability.
Explanation:To find the approximate probability that the total amount paid for the second movies will exceed $15.00, we need to use the expected value and standard deviation to calculate a z-score and then find the corresponding probability. First, we calculate the standard deviation using the formula: standard deviation = 0.15 * sqrt(30) = 0.2598.
Then, we calculate the z-score using the formula: z = (15 - 0.47) / 0.2598 = 57.05. Using a standard normal distribution table or a calculator, we find that the probability of getting a z-score greater than 57.05 is extremely close to 1.
Therefore, the approximate probability that the total amount paid for these second movies will exceed $15.00 is 0.91, option (a).
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All 231 students in the Math Club went on a field trip. Some students rode in vans which hold 7 students and some students rode in buses which hold 25 students each. How many of each type of vehicle did they use if there were 15 vehicles in total?
answer : 8 vans and 7 buses
In the figure below, what is the length of line BC? Photo provided
I can't see the photo ....
A wheel of 0.5 m radius rolls without slipping on a horizontal surface. The axle of the wheel advances at constant velocity, moving a distance of 20 m in 5 s. The angular speed of the wheel about its point of contact on the surface is:
The angular speed of the wheel at its point of contact on the surface is 8 radians per second.
Given that:
A wheel is rolling on a horizontal surface.
The radius of the wheel, r = 0.5 m
The velocity of the axle of the wheel is constant.
Here, the linear velocity can be found by taking the ratio of the distance to the time taken to cover that distance.
So, the linear speed is:
[tex]\text{v}=\frac{20}{5}[/tex]
[tex]=4 \text{ m/s}[/tex]
Now, the relationship between the angular speed and the linear speed is:
[tex]\omega=\frac{v}{r}[/tex]
[tex]=\frac{4}{0.5}[/tex]
[tex]=8[/tex] rad/s
Hence, the angular speed is 8 radians per second.
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The angular speed of the wheel about its point of contact on the surface is 8 rad/s.
To find the angular speed of the wheel about its point of contact on the surface, we can use the relationship between linear and angular velocity.
The linear velocity of a point on the wheel is given by:
v = ω * r
Where:
v is the linear velocity
ω is the angular velocity (angular speed)
r is the radius of the wheel
In this case, we know that the wheel rolls without slipping, which means the linear velocity of the point of contact with the surface is equal to the velocity of the axle. Since the axle moves a distance of 20 m in 5 s, the linear velocity can be calculated as:
v = 20 m / 5 s = 4 m/s
Given that the radius of the wheel is 0.5 m, we can rearrange the equation to solve for ω:
ω = v / r
ω = 4 m/s / 0.5 m
ω = 8 rad/s
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Describe how to use the vertical line test to determine if a graph is a function.
Using a ruler/straight edge to draw a vertical line for any values of x.If the curve is cut more than once, the graph is not for a function.
Step-by-step explanation:
Use a ruler to draw a line parallel to the y-axis for the taken values of x.When the vertical line is drawn, observe how the line intersect the graph. If the line intersects the graph more than once for nay value of x then that is not a graph of a function.
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Keywords: vertical line test, function, graph
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Kira goes running Monday, Wednesday, and Friday of each week. Each Monday she runs 2.5 miles, each Wednesday she runs 5.75 miles, and each Friday she runs 7.75 miles. How many total miles does she run in 9 weeks
Kira runs 144 miles in 9 weeks.
Step-by-step explanation:
Given,
Distance ran on Monday = 2.5 miles
Distance ran on Wednesday = 5.75 miles
Distance ran on Friday = 7.75 miles
Distance ran in one week = 2.5+5.75+7.75 = 16 miles
Distance ran in 9 weeks = Number of weeks * Distance ran in one week
Distance ran in 9 weeks = 16*9 = 144 miles
Kira runs 144 miles in 9 weeks.
Keywords: multiplication, addition
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Linear function f(x) = x is graphed on a coordinate plane. The graph of a new line is formed by changing the slope of the original line to 2/3 and the y-intercept to 4. Which statement about the relationship between these two graphs is true?a. The graph of the new line is steeper than the graph of the original line, and the y-intercept has been translated down.b. The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up.c. The graph of the new line is steeper than the graph of the original line, and the y-intercept has been translated up.d. The graph of the new line is less steep than the graph of the original line, and they-intercept has been translated down.
Answer:
b. The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up
Option b is right.
Step-by-step explanation:
Given that linear function f(x)=x is graphed on a coordinate plane.
The graph of a new line is formed by changing the slope of the original line to 2/3 and the y-intercept to 4.
The original slope was 1. Now changed to 2/3 i.e. slope is reduced. Hence the new line will be less steeper.
Also original line y =x has y intercept at the origin.
By changing y intercept to 4, we changed y intercept to upwards by 4 units.
Thus there is a vertical shift of 4 units.
b. The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up
Option b is right.
A linear function is represented by a straight line.
The true statement is: (b) the graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up.
The function f(x) is given as:
[tex]\mathbf{f(x) = x}[/tex]
The attributes of the new function are:
Slope = 2/3y-intercept = 4So, the new function is:
[tex]\mathbf{f'(x) = \frac23x + 4}[/tex]
The slope of [tex]\mathbf{f(x) = x}[/tex] is 1.
2/3 is less than 1.
So, the new line is less steep
The y-intercept (4) means that:
The new line is shifted up by 4 units
Hence, the correct statement is: (b)
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Hasn't worked two jobs last summer to start saving for a car he mowed lawns during the day and work at a pizza place in the evening with my cousin earn a total of $1400 if you earn 360 more at the pizza place the mowing one how much did he earn each job
Answer:
Hudson earned $520 in moving lawns and $880 by working in Pizza place.
Step-by-step explanation:
Given:
Total Money Earned = $1400
Let Money earned in moving lawns be 'x'
Also Given:
he earned $360 more at the pizza place than mowing lawns
Money Earned working at pizza place = [tex]x+360[/tex]
we need to find money earned in each job.
Now Total money earned is equal to sum of Money earned moving lawns and money earned working at pizza place.
Framing the equation we get;
[tex]x+x+360=1400[/tex]
Solving the equation we get;
[tex]2x+360 =1400\\\\2x = 1400-360\\\\2x =1040\\\\x=\frac{1040}{2}=\$520[/tex]
Money Earned working at pizza place = [tex]x+360 = 520 +360 = \$880[/tex]
Hence Hudson earned $520 in moving lawns and $880 by working in Pizza place.
Final answer:
To determine the earnings from each job, equations were set up using the total amount earned and the difference between the two earnings. The student earned $520 mowing lawns and $880 at the pizza place.
Explanation:
The student has provided information indicating that he worked two jobs and earned a combined total of $1400 over the summer. He earned $360 more at the pizza place than he did mowing lawns. To solve for how much he earned at each job, we need to set up two equations based on the given information. Let the amount earned mowing lawns be x and the amount earned at the pizza place be y.
From the information given, we have two equations:
x + y = $1400 (The total combined earnings) y = x + $360 (Earned $360 more at the pizza place than mowing lawns)Now we can substitute the second equation into the first to find how much he earned from each job. From the second equation, we have y = x + $360. Substituting this into the first equation gives us:
x + (x + $360) = $1400
Combining like terms gives us:
2x + $360 = $1400
Subtract $360 from both sides yields:
2x = $1040
Dividing both sides by 2 gives us:
x = $520
Therefore, the student earned $520 mowing lawns. To find how much was earned at the pizza place, we substitute x back into the second equation:
y = $520 + $360
So, the student earned $880 at the pizza place.
In the rectangular coordinate system, points (4,0) and (–4,0) both lie on circle C. What is the maximum possible value of the radius of C ?
Answer:
There is no finite maximum value of the radius of C.
Step-by-step explanation:
We have been given that in the rectangular coordinate system, points (4,0) and (–4,0) both lie on circle C. We are asked to find the maximum possible value of the radius of C.
If the center of the circle C would have been at origin (0,0), then the radius of the circle C would be 4 units.
Since there is no information given about center of circle, so radius can be infinitely long. Therefore, there is no finite maximum value of the radius of C.
2918+49
Which numbers should be used?
The estimated quotient is?
Answer: Use all numbers to add.
2918+49=2967
Estimated.... 2918+49 ≈ 3050
Hope this helps you out.
Answer:use all the numbers
Step-by-step explanation:
2918+49 ≈ 3050
Matthew has 63 pages to read in 2-5 days. He wants to read the same whole number of pages each day and the greatest number of pages in the fewest days possible. What is the best number of days for Matthew's reading plan?
Answer:
3
Step-by-step explanation:
63 can be factored as ...
61 = 1×63 = 3×21 = 7×9
The only plan that meets Matthew's requirement for number of days is to read 21 pages on each of 3 days.
Which of the following approaches is most suitable for auditing the finance and investment cycle?
Answer:
I would approach it with a graph or chart because that is the best way to go about a problem like this. don't quote me on this though because im only a freshmen in highschool. I hope this helps>
Step-by-step explanation:
Answer:
The question is not complete; the options are not given.
This is the complete question
Which of the following approaches is most suitable for auditing the finance and investment cycle?
a) perform extensive tests of controls and limit substantive procedures to analytical procedures
b) Ignore internal controls and perform extensive substantive procedures
c) Gain an understanding of internal controls and perform extensive substantive procedures
d) Ignore internal controls and limit substantive procedures to analytical procedures
Step-by-step explanation:
The right option is option c)
Gain an understanding of internal controls and perform extensive substantive procedures.
The approaches which is most suitable for auditing the finance and investment cycle is gaining an understanding of internal controls and perform extensive substantive procedures. Which makes option c the right option.
I NEED THE ANSWER FOR THIS TOO PLEASE
Answer:
Translated in numerical form: x - 2 ≤ 33.
The solution graph on a numbered line is shown in figure a.
The solution in a set notation: {x|x ≤ 35}
The solution in interval notation: (-∞, 35]
Step-by-step explanation:
"two less than a number is less than or equal to thirty three".
let's say the number is x.
Translated in numerical form: x - 2 ≤ 33.
Lets solve it:
x - 2 ≤ 33
x ≤ 33 + 2
x ≤ 35
The solution graph on a numbered line is shown in figure a.
The solution in a set notation: {x|x ≤ 35}
The solution in interval notation: (-∞, 35]
Keywords: inequality, graph
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HELP HELP HELP 100PTS
sin(x)= - 0.8. If x and y are complementary, what is cos(y)
Answer:
Step-by-step explanation:
[tex]sin (x)=-0.8\\x+y=90\\x=90-y\\sin(90-y)=-0.8\\cos (y)=-0.8\\sin (90-\alpha )=cos\alpha[/tex]
Answer:
cos x
Step-by-step explanation:
Can someone help me
Answer:
6 < x < 23.206
Step-by-step explanation:
To properly answer this question, we need to make the assumption that angle DAC is non-negative and that angle BCA is acute.
The maximum value of the angle DAC can be shown to occur when points B, C, and D are on a circle centered at A*. When that is the case, the sine of half of angle DAC is equal to 16/22 times the sine of half of angle BAC. That is, ...
(2x -12)/2 = arcsin(16/22×sin(24°))
x ≈ 23.206°
Of course, the minimum value of angle DAC is 0°, so the minimum value of x is ...
2x -12 = 0
x -6 = 0 . . . . . divide by 2
x = 6 . . . . . . . add 6
Then the range of values of x will be ...
6 < x < 23.206
_____
* One way to do this is to make use of the law of cosines:
22² = AB² + AC² -2·AB·AC·cos(48°)
16² = AD² + AC² -2·AD·AC·cos(2x-12)
The trick is to maximize x while satisfying the constraints that all of the lengths are positive. This will happen when AB=AC=AD, in which case the equations be come ...
22² = 2·AB²·(1-cos(48°))
16² = 2·AB²·(1 -cos(2x-12))
The value of AB drops out of the ratio of these equations, and the result for x is as above.
Answer 6<x<30:
Step-by-step explanation:
Suppose p(x) is a polynomial of smallest possible degree such that: bullet p(x) has rational coefficients bullet p(-3) = p(\sqrt 7) = p(1-\sqrt 6) = 0 bullet p(-1) = 8 determine the value of p(0).
Answer:
p(0) = 35
Step-by-step explanation:
-3, √7 and 1-√6 are all roots, hence, we can factorize (x-(-3)) = (x+3), (x-√7) and (x- (1-√6)) = (x-1+√6) from p. Since p has rational coefficients, then we need to cancel out both √7 and √6. To do so we should multiply by the rational conjugate, of the expressions (x-1+√6) and (x-√7), that means, where a square root of a non square positive number appears, place the opposing sign there.
The rational conjugate of (x-√7) is (x+√7), and
(x-√7)*(x+√7) = x²-7
On the other hand, the rational conjugate of (x-1+√6) is (x-1-√6), and
(x-1+√6) * (x-1-√6) = ( (x-1) + √6) * ((x-1) -√6) = (x-1)² - √6² = x²-2x+1-6 = x²-2x-5.
Thus, both x²-7 and x²-2x-5 are factors of p. The polynomial has the form
[tex]P(x) = c(x+3)(x^2-7)(x^2-2x-5)[/tex]
Where c is a constant. To determine c, we need to use the other piece of information given: p(-1) = 8
When we evaluate in -1, we get
[tex]p(-1) = c*(-1+3)((-1)^2-7)((-1)^2-2(-1)-5) = c* 2*(-6)*(-2) = c*24 = 8[/tex]
Thus, c = 8/24 = 1/3.
Therefore,
[tex]p(0) = \frac{1}{3} * (0+3)(0^2-7)(0^2-2*0-5) = \frac{1}{3}*3*(-7)*(-5) = 35[/tex]
I hope that works for you!
Write the equation of the line that passes through the point (–6, 2) and is parallel to the line whose equation is x = –10, then write the equation of the line that passes through the point (–6, 2) and is perpendicular to the line whose equation is x = –10.
a. x=-6, y=-6
b. x=-6, y=2
c. x=2, y=2
d. x=10, y=2
Answer:
B. x=-6, y=2
Step-by-step explanation:
Can someone please help me?? Im not quite sure how to get this answer.
What is the area of the shaded region in the figure below? Leave answer in terms of pi and in simplest radical form.
Answer:
C. 54π + 20.25√3 cm²
Step-by-step explanation:
The shaded area can be split into two areas: a sector and an isosceles triangle.
Area of a sector is:
A = (θ/360°) πr²
where θ is the central angle and r is the radius.
Area of an isosceles triangle can be found with SAS formula:
A = ½ ab sin θ
where a and b are two sides of a triangle and θ is the angle between them.
In this case, r = a = b = 9 cm. The central angle of the sector is 240°, and the vertex angle of the triangle is 120°. Therefore, the total area is:
A = (240°/360°) π (9 cm)² + ½ (9 cm) (9 cm) sin 120°
A = 54π + 20.25√3 cm²
Need help please!!! Just the numbers 4-7!
If the null hypothesis of an experiment is "The true mean weight of the piglets is at least 39lbs" what is the alternate hypothesis?
if its correct will give brainliest
Answer:
Alternate Hypothesis: The true weight of the piglets is greater than or equal to 39 lbs.
Step-by-step explanation:
Hypothesis testing is more like a binary process in which only one (Either Null or Alternate Hypothesis can be true) and we have to infer that whether our Null hypothesis is true or false.
The hypothesis testing involves following 4 general steps:
State the 2 hypothesis by making sure that they don't overlap with each otherDevelop the analysis plan or any statistical method to know whether the Null hypothesis should be accepted or rejectedExecute the developed plan and analyze the dataIn the end, after analyzing the data accept or reject the null hypothesisAs in the given question, if a number (X) is less than another number (Y) then it can't be less, equal or greater simultaneously.
AM i correct?
rational expression question
Answer:
[tex] \frac{16}{7(x + 4)} + \frac{5}{7(x - 3)} [/tex]
your answer is not correct.
The telephone pole is _____ feet tall. (Round to the nearest whole number)
14 ft
42 ft
33 ft
85 ft
Answer:
33 ft
Step-by-step explanation:
sin( angle ) = opposite / hypotenuse
Captain salamander is collecting Christmas trees to sell to the market. He collects 31 trees. He sells all his trees to 3 of his friends. Frazer has 3 more trees than Sally. Sally has 7 fewer trees than Flame. How many trees do each of his friends each get
Answer:
Flame has 14 trees, Sally has 7 trees and Frazer has 10 trees.
Step-by-step explanation:
Given;
Total Trees = 31
Let the number of trees Flame has be 'x'.
Now given:
Sally has 7 fewer trees than Flame.
framing in equation form we get;
Number of trees Sally has = [tex]x-7[/tex]
Also Given:
Frazer has 3 more trees than Sally.
framing on equation form we get;
Number of trees Frazer has = [tex]x-7+3 = x-4[/tex]
Now We know that Captain salamander total trees in 3 friends.
Hence we can say that;
Total Number of trees is equal to sum of number of trees Flame has and Number of trees Sally has and Number of trees Frazer has.
framing in equation form we get;
[tex]x+(x-7)+(x-4)=31\\\\x+x-7+x-4=31\\\\3x-11=31\\\\3x=31+11\\\\3x = 42\\\\x = \frac{42}{3} = 14[/tex]
Hence Number of trees Flame has = 14 trees
Number of trees Sally has = [tex]x-7 = 14-7 =7 \ trees[/tex]
Number of trees Frazer has = [tex]x-4 = 14-4 = 10 \ trees[/tex]
Hence Flame has 14 trees, Sally has 7 trees and Frazer has 10 trees.