The dimensions of furniture in a rectangular bedroom in my scale drawing is equals to the 18 in. by 21 in.
To draw dimensions on scale drawing :
Determine the scale on the drawing . Using the ruler, measure the distance present on the drawing.Multiply the distance we measure by the scale to particular the distance in real life.I want to a scale drawing of my bedroom which help me to arrange my furniture.
Dimensions of rectangular bedroom= 12 ft by 15 ft
that is length of room, l = 15 ft
width of rectangle room, w = 12 ft
Area of rectangular bedroom = l×w = 12 × 15
= 180 ft²
scale of furniture = 3 in. = 2 ft
=> 2 ft = 3 in
=> 1 ft = 3/2 in
Now 12 ft by 15 ft in inches :
=> 12 × 3/2 in by 15 × 3/2 in
=> 18 in by 22.5 in
Hence, required dimensions are 18 inches by 22.5 inches.
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33. Solve the equation and check your solution: -2(x - 1) = 2 - 2x
Answer:
this equation is always true
Step-by-step explanation:
Solve the equation and check your solution: -2(x - 1) = 2 - 2x
-2(x - 1) = 2 - 2x
-2x + 2 = 2 - 2x
-2x + 2x = 2 - 2
0 = 0
(this equation is always true)
------------------------------
check
whatever value you give to x the equation is always true, let's take 2 as an example
-2(2-1) = 2 - 2 * 2
-4 + 2 = 2 - 4
-2 = -2
If tan theta equals 4/3 on the interval (pi, 3pi/2), find sin 2 theta, cos 2 theta, tan 2 theta
With the value tanθ = 4/3 on the interval (π, 3π/2), using trigonometric identities sin 2θ = 24/25 , cos 2θ = -7/25 , tan 2θ = -8/7.
First, we'll find sin 2θ:
sin 2θ = 2sinθcosθ
We can use the identity tanθ = sinθ/cosθ to find sinθ and cosθ:
sinθ = 4/5 and cosθ = 3/5
So,
sin 2θ = 2(4/5)(3/5) = 24/25
Next, we'll find cos 2θ:
cos 2θ = cos^2θ - sin^2θ = 1 - 2sin^2θ
Using the values of sinθ and cosθ that we found earlier:
cos 2θ = 1 - 2(4/5)^2 = 1 - 32/25 = -7/25
Finally, we'll find tan 2θ:
tan 2θ = (2tanθ)/(1 - tan^2θ)
Using the value of tanθ that we were given:
tan 2θ = (2(4/3))/(1 - (4/3)^2) = (8/3)/(-7/9) = -8/7
So, the values of sin 2θ, cos 2θ, and tan 2θ are:
sin 2θ = 24/25
cos 2θ = -7/25
tan 2θ = -8/7
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# 25 i
You buy 6 balloons and 3 banners for $15. Your friend buys 4 balloons and 1 banner for $9. What is the cost of each balloon? of each
banner?
Each balloon costs $
Save / Exit
and each banner costs $
The cost of each balloon and each banner is $2 and $1 respectively.
What is the cost of each balloon and banner?Let
cost of balloon= x
cost of banner= y
6x + 3y = 15
4x + y = 9
Multiply equation (2) by 3
12x + 3y = 27
6x + 3y = 15
12x + 3y = 27
Subtract the equations to eliminate y
12x - 6x = 27 - 15
6x = 12
divide both sides by 6
x = 12/6
x = $2
Substitute into
4x + y = 9
4(2) + y = 9
8 + y = 9
y = 9 - 8
y = $1
Therefore, each balloon cost $2 and each banner cost $1
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Sofie makes and sells scarves. Her profit depends on what price she charges for a scarf. She writes the expression (x−5)(50−2x) to represent her profit based on the price per scarf, x . Enter Sofie's average change in profit for two different sections of the graph.
Sofie will not make a profit if she sells her scarves for $5 or less.
The maximum profit Sofie can make is $200.
What is a Parabola?A parabola is a plane curve created when a point moves in such a way that the distance it travels from a fixed point to a fixed line.
According to the given problem,
y = (x - 5)(50 - 2x)
⇒ y + (-(x - 5)(50 - 2x) = (x - 5)(50 - 2x) + (-(x - 5)(50 - 2x)
⇒ y - (x - 5)(50 - 2x) = (x - 5)(50 - 2x) - (x - 5)(50 - 2x)
⇒ y - (x - 5)(-2x + 50) = 0
⇒ y - (-x *2x + x*50 + 5*2x -5*50) = 0
⇒ y - ( -2x² + 50x + 10x - 250) = 0
⇒ y - ( - 2x² + 60x - 250 ) = 0
⇒ y + 2x² - 60x + 250 = 0
⇒ 2x² -60x + y + 250 = 0
⇒ ( 2x² - 60x ) + y + 250 = 0
⇒ 2 ( x² - x) + y + 250 = 0
⇒ 2 ( x² - x) + y + 250 = 0
⇒ 2 ( x² - 30x ) + y + 250 = 0
⇒ 2( x² + 2(-15)x + 225 -225 +y + 250 = 0
⇒ 2( x - 15 )² + 2(-225) + y + 250 = 0
⇒ 2( x - 15 )² + y = -2(-225) - 250
⇒ 2( x - 15 )² + y = 450 - 250
⇒ 2( x - 15 )² + y = 200
⇒ y = -2( x - 15 )² + 200
This equation is in the form of y = a(x - h)² + k where the vertex of the parabola is (h , k).
Therefore the vertex of the parabola is at (15 , 200)
Hence, we can conclude that Sofie will maximum profit of $200 if she sells a scarf at 15$ and will make the least profit if she sells the scarf at $5 or less.
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easyyyy but um.. please help QvQ
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
in our case
9.3 × 3.5 / 2 = 16.275 ft²
as you can see, yes, really easy.
what was the problem ? do you need any further explanation ?
what is thhe sales tax on $58 at a rate of 5.5%
Answer:
3.19
Step-by-step explanation:
5.5% of 58 is 3.19
and is you need it,
58 - 3.19 = 54.81
I believe this is right
the sales tax on $58 at a rate of 5.5% is $3.19
How to find the tax on $58 at a rate of 5.5%?
Taxes are a mandatory contribution to the state. So sales must pay taxes, and it is stated that the rate of tax that must be paid is 5.5%
The way to calculate tax from sales is to multiply the tax rate by the income from sales.
the income = $58
the rate of tax = 5.5%
the tax to be paid by sales = the income x the tax
= $58 x 5.5%
= $3.19
so the answer to the question is $3.19
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Beatriz Cruz purchased a home for $98,500. She made a $28,500
down payment and mortgaged the rest. Her annual expenses
for mortgage interest, taxes, repairs, insurance, and depreciation
totaled $6,890. She rented the house for $750 a month.
a. What is the annual net income?
b. What is the annual yield?
e. What monthly rent would she have to charge to get
a yield of 90%?
Answer:
a. To find the annual net income, subtract the annual expenses from the annual rental income.
The annual rental income = $750 * 12 months = $9,000
So, the annual net income = $9,000 - $6,890 = $2,110
b. To find the annual yield, divide the annual net income by the investment cost (the down payment) and multiply by 100 to get the answer as a percentage.
The annual yield = ($2,110 / $28,500) * 100 = 7.41%
c. To find the monthly rent required to get a yield of 90%, divide the investment cost by the desired yield and divide by 12 to get the monthly rent.
The investment cost = $28,500
The desired yield = 0.90
So, the monthly rent = ($28,500 / 0.90) / 12 = $2,306.25
Step-by-step explanation:
To the nearest tenth, what is the length of the hypotenuse of an isosceles right triangle with a leg of 7 8 inches?
The length of the hypotenuse of the isosceles right triangle is 2.8 inches.
What is isosceles right triangle?
An isosceles right triangle is a right triangle with two equal sides. In this case, the two equal sides are each 7 8 inches long.
To find the length of the hypotenuse, we can use the Pythagorean theorem:
a^2 + b^2 = c^2, where c is the length of the hypotenuse
In this case, a = b = 7/8 inches, so:
(7/8)^2 + (7/8)^2 = c^2
(49/64) + (49/64) = c^2
98/64 = c^2
c = sqrt(98/64) inches
To the nearest tenth, c = 2.8 inches, so the length of the hypotenuse of the isosceles right triangle is 2.8 inches.
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To solve 3x = 9, we divide each side of the equation by
Answer: x=3
Step-by-step explanation:
divide by the common factor 3
3x ÷ 3 = x
9÷3 = 3
hence the reason we get x=3
Answer: 3
Step-by-step explanation:
To solve for x, you need to divide 9 by 3 which equals 3.
Since 3x = (3 ⋅ 3), x = 3.
y=4x^2-56x is the equation of a curve.
by completing the square, show that the co-ordinates of the turning point are (7,-196)
Answer:
[tex]y=4(x-7)^2-196[/tex]
Step-by-step explanation:
Given quadratic equation:
[tex]y=4x^2-56x[/tex]
Completing the squareFactor out the coefficient of the term x²:
[tex]y=4(x^2-14x)[/tex]
Add and subtract the square of half the coefficient of the term in x inside the brackets:
[tex]y=4\left(x^2-14x+\left(-\dfrac{14}{2}\right)^2-\left(-\dfrac{14}{2}\right)^2\right)[/tex]
Simplify:
[tex]y=4\left(x^2-14x+\left(-7\right)^2-\left(-7\right)^2\right)[/tex]
[tex]y=4\left(x^2-14x+49-49\right)[/tex]
Factor the perfect square trinomial created by the first three terms inside the brackets:
[tex]y=4\left((x-7)^2-49\right)[/tex]
Distribute:
[tex]y=4(x-7)^2-196[/tex]
Turning pointThe equation is now in vertex form y = a(x - h)² + k, where (h, k) is the vertex of the parabola (turning point).
Compare the equation with the vertex formula to identify the values of h and k:
h = 7k = -196Therefore, the coordinates of the turning point (vertex) are (7, -196).
in ∆XYZ, the measures of angles X, Y, and Z, respectively, are in the ratio 1:10:25. Find the measure of each angle.
m
m
m
The measures of the angles X, Y, and Z are 5, 50, and 125 degrees.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that in ∆XYZ, the measures of angles X, Y, and Z, respectively, are in the ratio 1:10:25.
We have to find the measure of each angle.
Let the measures can be expressed as 1x, 10x, and 25x, respectively, where x is an arbitrary value.
We know that the sum of the angles of a triangle is always 180 degrees, so:
1x + 10x + 25x = 180
36x = 180
Divide both sides by 36
x = 5
Therefore, the measures of the angles X, Y, and Z are 5, 50, and 125 degrees.
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Des can choose between two jobs: Job A pays £3.80 per hour for 40 hours per week, Job B pays £4.50 per hour for 32 hours per week. For which job will Des earn the most money per week?
The solution is, For job- A will Des earn the most money per week.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Job A pays £3.80 per hour for 40 hours per week,
Job B pays £4.50 per hour for 32 hours per week.
for, job A - he earns = £3.80 * 40
= £ 152 pe week
and, for job B - he earns = £4.50 * 32
=£ 144 per week.
Hence, The solution is, For job- A will Des earn the most money per week.
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it is known that a certain drug causes side effects in 12 12 % of patients. if we consider a random sampling of 12 12 patients, what is the probability less than two have the side effect?
By applying binomial distribution formula, it can be concluded that the probability less than two have a side effect is 56.86%.
Binomial distribution is the discrete probability distribution of the number of successes or failures in n independent trials, where each trial result has a probability p.
P(x) = C(n,x) · pˣ · qⁿ⁻ˣ where:
C = number of combinations
p = probability of success
q = probability of failure
x = number of times for a specific outcome within n trials
n = number of trials
We have the following information:
p = 12% = 0.12, thus:
q = 1 - p
= 1 - 0.12
= 0.88
n = 12
We want to find the probability less than two have the side effect, P(x<2):
P(x<2) = P(0) + P(1)
= (C(12,0) · 0.12⁰ · 0.88¹²) + (C(12,1) · 0.12¹ · 0.88¹¹)
= (1 · 1 · 0.2157) + (12 · 0.12 · 0.2451)
= 0.2157 + 0.3529
= 0.5686 ≈ 56.86%
Thus, the probability less than two have the side effect is 56.86%.
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ATTACHMENTTTTTTTTTTTTTTTTTTTT
a. The total of the two sides of the right triangle using Algebraic expression is 3x²+7x-4.
b. The length of the missing side of the triangle is 3x³-4x²-15x+5.
c. If the value of x=2, then the length of the three sides of the triangle is
a=11, b=11 and c= -17.
d. No, it is not possible to have these side lengths for a right triangle.
Define AlgebraAlgebra is a discipline of mathematics that studies symbols and the mathematical operations that can be applied to them. These symbols are referred to as variables because they don't have predetermined values. These values are usually represented in algebra by variables, which are symbols like x, y, z, p, or q. These symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations in order to ascertain the values.
a. Let the sides of the right triangle be a, b and c.
Given, one side of the triangle is 2x² + 2x - 1 and
another side is 5x + x² -3.
So, let a = 2x²+2x-1 and b = 5x+x²-3
Now, the total of the two sides= a+b
a+b
=2x²+2x-1 + 5x+x²-3
= 3x²+7x-4
Therefore, the total of the two sides of the right triangle = 3x²+7x-4.
b. Now the perimeter of the triangle is given= 3x³-x²-8x+1.
Given, a+b+c=3x³-x²-8x+1.
We already have a+b, so by simplifying the equation a+b+c=3x³-x²-8x+1
we can find the length of the third side, c.
a+b+c= 3x³-x²-8x+1
⇒3x²+7x-4 +c= 3x³-x²-8x+1
⇒c= 3x³-x²-3x²-8x-7x+1+4
⇒c= 3x³-4x²-15x+5.
Therefore, length of the missing side is 3x³-4x²-15x+5.
c. We have the three sides of the triangle with us which are:
a = 2x²+2x-1
b = 5x+x²-3
c = 3x³-4x²-15x+5
Now putting the value of x as 2 in the equations as follows:
a= 2(2²) +2(2)-1
= 8+4-1
=11
b=5(2) +2²-3
= 10+4-3
=11
c=3(2³)- 4(2²) -15(2) +5
=24-16-30+5
= -17
Therefore, the length of the three sides of the right triangle
are 11, 11 and -17.
d. The sides of the right triangle are.
a = 11
b = 11
c = -17
We know as per the Pythagorean theorem c² = a² + b².
Accordingly, c²= 289 & a² = 121 and b²= 121, a² + b²= 242
which shows that c² is not equal to a² + b².
As, the sides of the triangle does not follow the Pythagorean theorem, so these are not the sides of a right-angle triangle.
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Poseidon is in search for Zeus' lightning bolt after being accused of theft! Rumored to have
been among the luggage of a luxury cruiser that has disappeared, the god of the sea is
desperately searching the Bermuda Triangle: Given the approximate boundary of missing ships,
how much area is Poseidon searching?
GEORGIA
SOUTH
CAROLINA
FLORIDA
10-9-8-7-6-5-3-2
Cuba
9
946
S
43
2
0123
2 3 4 5 6 7 8 9 10
Dominican
Republi
Puerto Rico
The approximate area that Poseidon is searching is given as follows:
64.13 square units.
How to obtain the area of the triangle?The area of a triangle is given by half the multiplication of the base length by the height.
The coordinates of the vertices of the triangle in this problem are given as follows:
(-6,1), (4,-5) and (-1,9).
Any of the three sides can be chosen as the base, and we use the equation for the distance between two points to obtain it's length.
Choosing vertices (-6,1) and (4,-5) as the base, it's length is given as follows:
b = sqrt((4 - (-6))² + (-5 - 1)²)
b = 11.66.
The midpoint of the base has the coordinates given as follows:
x = (-6 + 4)/2 = -1.y = (1 - 5)/2 = -2.The height is the distance between the vertices (-1,-2) and (-1,9), hence, as they have the same x-coordinate, the height is given as follows:
h = 9 - (-2)
h = 11.
Then the area is given as follows:
A = 0.5 x 11.66 x 11
A = 64.13 square units.
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Emily buys 6 cans of beans for $1.50 each. She also buys a pineapple, The total cost of the item is $12.30. HURRY PLS :) THANK YOU BTW! :)
Answer:
$3.30
Step-by-step explanation:
6 x 1.50 = 9
12.30 - 9 = $3.30
Whotube, the who’s who of online video sites, has offered to pay for a free trip to its headquarters for anyone who has posted an original viral video. To qualify as viral, a video must be viewed by at least one million people within two hours of being posted, not including the initial post.
Taylor, a self-proclaimed mathemagician, posts a video of a dancing log (one with rhythm) to Whotube at 10 p.m. Three arborists, devoted to their profession, immediately watch the video. Enamored with such a cutting edge clip, they each share it with three other tree trimming friends every five minutes, each of whom views and shares the video with three more friends every five minutes, and so on. They continue sharing the video this way until 10:20, at which point they all get distracted by a video of a campfire and immediately stop viewing and sharing.
Over the next four minutes, thirty fellow mathemagicians discover and view the video. This incredible phenomenon continues at a constant rate of thirty views by mathemagicians every four minutes until 11:32 p.m. at which point almost all of the mathemagicians in the world have viewed the video.
Then, the real magic happens when Kimmy Schmallon mentions it on the Late Night Show. Once it is mentioned on the Late Night Show at 11:32 p.m., the current number of views doubles every three minutes. This continues until the end of the show at 1 a.m.
Will Taylor get invited to Whotube headquarters? Use multiple representations to justify your conclusion.
Answer:
yes
Step-by-step explanation:
Taylor will get an offer for a free trip as within two hours (10 - 12) even before the end of the midnight show, he got the required views.
from 10: to 10:20
1 : 3
3: 3 in every five minutes i.e. 10:25, 10:30, 10:35 n so on
1: 30 in every four minutes
till 11:32
from 11:32 till 12:00
the views recorded till now doubles every three minutes!!
Practice 9. Expressing the future in time clauses. (Chart d-3)
Complete the sentences with the correct form of the verb.
1. Grandma and Grandpa are planning to travel often when they (retire)
2. I'll wake up tomorrow morning when the alarm clock (ring)
3. The students will relax after they (finish)
4. You'll feel a lot better after you (take)
this medicine.
5. The residents of the coastal areas will prepare for the hurricane before it
(arrive)
6. Mark will work in a law firm as soon as he (graduate)
school.
7. We'll have dinner as soon as the rice (be)
8. I'll tell you as soon I (hear)
9. Before we (leave)
10. We'll start our newspaper delivery again after we (get)
their final exams.
ready.
from law
any news.
on vacation, we'll stop our newspaper delivery.
back from vacation.
The chance at least one of the alarms will wake her up is 0.96.
What is the probability of both independent events?If the probability of one event does not affect the probability of another event, the events are independent.
Given
Probability that Alarm clock 1 is reliable = 60% = 0.60
Probability that Alarm clock 2 is reliable = 90% = 0.90
P of alarm clock 1 not reliable = 0.40
P of alarm clock 2 not reliable = 0.10
Therefore,
The chance at least one of the alarms will wake her up is;
=p1.p2' + p1'. p2 + p1.p2
so, calculating we get,
= 0.96
Hence, the chance at least one of the alarms will wake her up is 0.96.
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a box contains 6 blue blocks, 13 yellow blocks, 15 blue spheres, and 17 yellow spheres. what is the probability you draw a sphere given it is blue?
The probability that you draw a sphere given that it is blue is given as follows:
5/7.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
The total outcomes in this problem are the blue shapes, hence the number is given as follows:
6 + 15 = 21 shapes.
The desired outcomes are the blue spheres, hence the number is given as follows:
15.
Hence the probability that you draw a sphere given that it is blue is given as follows:
p = 15/21
p = 5/7. (simplify numerator and denominator by 3).
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help i will give alot of points
Answer:east
Step-by-step explanation:
north: LOW:-8F HIGH:10F this have the most change
+18F
south: LOW:-3F HIGH:2F this have the third most change
+5F
east: LOW:-2F HIGH:0F this have the least change
+2F
west: LOW:-4F HIGH:3F this have the second most change
+7F
the east only have +2F so it have the least change
A back-to-school sale offered a laptop for $379. This sale price reflected a 15% discount.
Use the equation to find the cost of the computer before the reduction in price.
(Round to the nearest cent as needed.)
If a back-to-school sale offered a laptop for $379 and this sale price reflected a 15% discount, after using the equation the cost of the computer before the reduction in price is, $446.47.
What is percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
Let's call the original cost of the laptop "x".
The equation to find the cost after a discount is:
x - x * (discount rate) = sale price
In this case, the discount rate is 15%, or 0.15. Plugging in the given values:
x - x * 0.15 = 379
Expanding the equation:
x - 0.15x = 379
0.85x = 379
Dividing both sides by 0.85:
x = 379 / 0.85
x = 446.47
So, the cost of the laptop before the reduction in price was $446.47.
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Calculate P(3, 2) Help
12
8
7
6
6
Hope This Helps!
P2 = 90; 10P2 = 90. Combinations. There are also two types of combinations
Answer:
P(3, 2) = 6
Step-by-step explanation:
A permutation is an ordered combination, i.e. an arrangement in a definite order of a number of objects taken some or all at a time.
Permutation formula[tex]P(n,r)=\dfrac{n!}{(n-r)!}[/tex]
where:
n is the number of objects to choose from.r is the chosen number of objects.0 ≤ r ≤ nGiven P(3, 2):
n = 3r = 2So we need to calculate the permutations of two numbers taken from three numbers.
The numbers are 1, 2 and 3. As order matters, the number of ways two numbers from this set can be arranged is:
1 and 21 and 32 and 12 and 33 and 13 and 2Therefore, there are 6 ways two numbers from the set of three numbers can be arranged.
To prove this, substitute n = 3 and r = 2 into the permutation formula:
[tex]\begin{aligned}\implies P(3,2)&=\dfrac{3!}{(3-2)!}\\\\&=\dfrac{3!}{1!}\\\\&=\dfrac{3 \times 2 \times 1}{1}\\\\&=\dfrac{6}{1}\\\\&=6 \end{aligned}[/tex]
Therefore, P(3, 2) = 6.
The marketing club school is openings student store. They randomly survey 50 students who how much money they spend
onunch each day. What is the expected value for a student to spend on lunch each day?
Student Lunch Survey
Number of Dollars spent on
Students
Lunch Eschwy
510
SSS
05. 18
5. 07
See
signou
us
247
The Expected value is the long-term average position of any variable. The anticipated value will be$5.18
The predicted value is the long-run average of all variables. It also shows the loaded normal probabilities for all possible values. Investors use expected value to estimate an investment's return, often in relation to its risk.
Given the data in detail
Pupil Lunch check Bones spent Probability
2$10 20/50.
1$8 8/50.
12$6 72/50.
23$5 115/50.
8$4 32/50.
4$3 12/50
The sum will be
aggregate = 20+ 8 +72 +115 +32 +12
50
= 259/50
= $5.18
The anticipated value a pupil would spend on lunch each day will be $5.18
Question
From the following data, calculate the expected value a pupil can spend on lunch each day?
Students & Amount spent
2$ 10
1$ 8
12$ 6
23$ 5
8$ 4
4$ 3
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A boat is heading towards a lighthouse, whose beacon-light is 107 feet above the water. From point
�
A, the boat’s crew measures the angle of elevation to the beacon, 12
∘
∘
, before they draw closer. They measure the angle of elevation a second time from point
�
B at some later time to be 20
∘
∘
. Find the distance from point
�
A to point
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B. Round your answer to the nearest foot if necessary.
The distance between the points A and B is 209.4 feet
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.
A boat is heading towards a lighthouse, whose beacon-light is 107 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 12°. Let a represent distance from point A to light house:
tan(12) = 107/a
a = 503.4 feet
They measure the angle of elevation a second time from point B at some later time to be 20°. Hence, if b represent distance from point A to light house:
tan(20) = 107/b
b = 294 feet
Distance from point A to B = 503.4 feet - 294 feet = 209.4
The distance between the points is 209.4 feet
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A triangle has side lengths 4 inches 5 inches and 7 inches Is the triangle a right triangle?
Answer:
Step-by-step explanation:
To determine if the triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's label the sides of the triangle as follows:
a = 4 inches
b = 5 inches
c = 7 inches
Using the Pythagorean theorem, we can calculate:
c^2 = a^2 + b^2
7^2 = 4^2 + 5^2
49 = 16 + 25
49 = 41
Since 49 does not equal 41, this means that the triangle is not a right triangle.
Therefore, the answer is no, the triangle is not a right triangle.
the points of this 3-by-3 grid are equally spaced horizontally and vertically. how many different sets of three points of this grid can be the three vertices of an isosceles triangle?
The number of different sets of three points of this grid can be the three vertices of an isosceles triangle is 36.
An isosceles triangle is one with two equal sides. The two angles that face the two equal sides are also equal. An isosceles triangle, in other words, is a triangle whose two sides are equal in length.
By using the Permutation formula,
Number of isosceles triangle to be formed is,
9!/(7!x2!) = 9x8x7!/7!x2!
= 9x8/2
= 36
So number of isosceles triangle that can be formed of this 3-by-3 grid is 36.
When a square is described as a 3 x 3 Magic square, it has three rows and three columns. An illustration of a 3 by 3 magic square with the magic constant.
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1.(2x+y) (4x-9)
2.(3x+5y2
3.(x-2) (x2-x+3)
Answer:
x³ - 3x² + 5x - 6
Step-by-step explanation:
Multiplication of algebraic expression:1) (2x + y)(4x - 9) = 2x*(4x - 9) + y(4x - 9)
= 2x*4x - 2x*9 + y*4x - y *9
= 8x² - 18x + 4xy - 9y
2) (3x + 5y)²
Identity : (a + b)² = a² + 2ab + b²
a = 3x and b = 5y
(3x +5y)² = (3x)² + 2 * 3x *5y + (5y)²
= 9x² + 30xy + 25y²
3) (x -2)(x² - x + 3) = x*(x² - x + 3) - 2(x² - x + 3)
=x*x² - x*x + x*3 -2*x² + 2*x - 2*3
= x³ - x² + 3x - 2x² + 2x - 6
=x³ - x² - 2x² + 3x + 2x - 6
Combine like terms. Like terms have same variable with same exponent.
= x³ - 3x² + 5x - 6
confused about this
Answer:
d
Step-by-step explanation:
d
helpppppppp please, i would like some help so i dont have to do it later lol
Given all sides are right angles, the height of the sides are equal.
left side = 12
right side = x+5
set equation equal to each other and solve for x.
12 = x +5 =>> 12-5 = x =>> x = 7
x = 7 cm
Hi,what is 9/10 divided by 3/5
The value of 9/10 divided by 3/5 is 3/2.
How to multiply two fractions?
When multiplying fractions, you first start with the two fractions you want to multiply. You multiply the numerators (the top numbers) together, and then multiply the denominators (the bottom numbers) together. After putting the two results together as a new fraction, you may need to simplify the fraction in order to express it in its lowest terms.
Firstly , let's find the reciprocal of the divisor
Reciprocal of
3/5 is 5/3
Now, multiply it with the dividend
So,
9/10 ÷ 3/5
= 9/10 × 5/3
= 45/30
After reducing the fraction, the answer is
3/2
Hence , the value of 9/10 divided by 3/5 is 3/2.
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