This follows from the identity
[tex]\cot(x) = \dfrac1{\tan(x)} = \tan(90^\circ - x)[/tex]
The overall product is 1 because
[tex]\tan(10^\circ) \tan(80^\circ) = \cot(80^\circ) \tan(80^\circ) = 1[/tex]
[tex]\tan(20^\circ) \tan(70^\circ) = \cot(70^\circ) \tan(70^\circ) = 1[/tex]
[tex]\tan(30^\circ) \tan(60^\circ) = \cot(60^\circ) \tan(60^\circ) = 1[/tex]
[tex]\tan(40^\circ) \tan(50^\circ) = \cot(50^\circ) \tan(50^\circ) = 1[/tex]
math related pls help
Hello and Good Morning/Afternoon:
Let's take this problem step by step:
Let's consider what the problem wants:
⇒ the value of (f-g)(y)
Let's consider what the problem gives us:
⇒ the value of f(y) and g(y)
Let's consider the relationship between f(y), g(y) and (f-g)(y)
⇒ [tex](f-g)(y)=f(y)-g(y)[/tex]
Let's solve for (f - g)(y)
[tex]\hookrightarrow(f-g)(y) = f(y)-g(y) = 5y^2-2y+1-(-3y^2-y-2)\\=5y^2-2y+1+3y^2+y+2=8y^2-y+3[/tex]
Answer: 8y²- y + 3
Hope that helps!
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nevan typed 110 words in 2 2/4 minutes. at this rate.how many words can he
type in 4 1/4
Answer:
ther will be 240 words in 4 1/4
Answer:
187 words.
Step-by-step explanation:
His rate of typing = 110 / 2 2/4
= 110 / 2.5
= 44 words / minute.
So in 4 1/4 minutes he will type
44 * 4 1/4
= 176 + 11
= 187 words.
If the original recipe made 14 pancakes and the cafeteria plans to charge $.50 per pancake, how much money will they make if they sell all of the
If they sell all the pancakes, they will win $7
how much money will they make if they sell all of the pancackes?
We know that they can make a batch of 14 pancakes, such that each one can be sold for $0.50
Then the total amount that they get if they sell all the pancakes is given by the product:
P = 14*$0.50 = $7
If they sell all the pancakes, they will win $7
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Which of the following values is not a perfect square?
a.81
b.125
c.49
d.100
Answer: b. 125
Step-by-step explanation:
Find the square roots of each, and if the square root is a decimal, it is not a perfect square.
Square root of 81: 9
Square root of 49: 7
Square root of 100: 10
That leaves 125.
Jay went to an amusement park. the park charges an entrance fee of $10.50 and $4.50 for every ride. jay spent $46.50 on entrance fees and rides. which fuction can be used to find the number of rides he went on? f (x) = 4.5 x + 10.5 f (x) = 4.5 x f (x) = 4.5 x minus 10.5 f (x) = negative 4.5 x
The function that can be used to find the number of rides Jay went on is, f(x) = 4.5x + 10 = 46.5. Hence, the first option is the right choice.
Also, on solving the function we get that, Jay went on 8 rides.
We assume the number of rides Jay spent to be x.
The cost of each ride is given to be $4.50.
Thus, the total amount Jay spent on rides = $4.50x.
The entrance fee to the park is given to be $10.50.
Thus, the total expenditure of Jay can be shown as $(4.5x + 10.5).
But, in the question we are given that Jay spend $46.50 altogether.
Thus, the function to find the number of rides Jay went on can be shown as:
f(x) = 4.5x + 10 = 46.5.
Hence, the first option is the right choice.
To find the number of rides he went, we can solve this function as:
4.5x + 10 = 46.5,
or, 4.5x = 46.5 - 10.5 = 36,
or, x = 36/4.5 = 8.
Thus, Jay went on 8 rides.
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Which of the statements below is true for the following set of numbers?42,10,36,51,70,28
Answer:
statement 1(one)
Step-by-step explanation:
A graphing calculator is recommended.
Use the graphical method to find all solutions of the system of equations, rounded to two decimal places.
y=e^x+e^-x
y=5-x^2
Dont bother answering if you won't show how you got it
The solution to the system of equations is (-1.189, 3.587) and (1.189, 3.587)
How to solve the system of equations?The system of equations is given as
y=e^x+e^-x
y=5-x^2
See attachment for the graph of both equations
From the attached graph, the curve intersect at
(-1.189, 3.587) and (1.189, 3.587)
Hence, the solution to the system of equations is (-1.189, 3.587) and (1.189, 3.587)
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if the price of an object with 13% vat is Rs 5650 find the net price of the object
Find the surface area of the prism. Round to the nearest tenth if necessary.
Answer:
480
Step-by-step explanation:
First, lets solve for the area of the 3 rectangles in the prism
One can be found by doing 17*9. The other, 8*9, the last 15*9
Next, lets solve for the 2 triangles. This is found with...
1/2(8)(15). This turns out to be 60, and we multiply that by 2 since there are 2 of those triangles.
Add everything up:
72+153+135+120 = 480
Surface=
Area=
Help please thanks
Surface area of the rectangular solid = 416 in.².
Volume = 480 in.³.
What is the Surface Area and Volume of a Rectangular Solid?Surface area = 2(wl+hl+hw)
Volume = (length)(width)(height).
Given the following:
Length (l) = 12 in.
Width (w) = 10 in.
Height (h) = 4 in.
Surface area = 2(wl+hl+hw) = =2·(10·12+4·12+4·10) = 416 in.².
Volume = (12)(10)(4) = 480 in.³.
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ppppp-pp help please.
Answer:
There are two complex roots:
[tex]-3\pm i[/tex]============
Given equation:x² - 6x + 10 = 0The standard form is:
ax² + bx + c = 0Compared we can find values of the coefficients and the constant:
a = 1, b = - 6, c = 10Substitute these values into quadratic formula:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
and work out roots:
[tex]x=\dfrac{-(-6)\pm\sqrt{(-6)^2-4*1*10} }{2*1}=x=\dfrac{6\pm\sqrt{36-40} }{2}=\dfrac{6\pm2\sqrt{-1} }{2}=3 \pm i[/tex]
A shipment of 60 highly sensitive accelerometers is to be accepted or rejected based on the testing of 5 chosen randomly from the lot. The shipment will be rejected if more than 1 of the 5 fail. It is known that 10% of the shipment does not meet the specifications. Let X denote the number of units that fail.
The value of X that number of unit fails are 1/12.
According to the statement
we have a given that the there is a shipment of 60 highly sensitive accelerometer. And there is a testing of randomly 5 accelerometers.
And we have to find that the how much units that fails in the specifications.
So,
We find the value of X by use of Probability.
The probability that unit fails = number of units that chosen randomly / total units.
So, substitute the values in it then
The probability that unit fails = 5 / 60
The probability that unit fails = 1 / 12.
The probability that unit fails from 60 accelemoters is 1 / 12.
So, The value of X that number of unit fails are 1/12.
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At the movie theatre, child admission is and adult admission is . On Wednesday, tickets were sold for a total sales of . How many child tickets were sold that day
The child tickets were sold that day is 82.
Given the cost of child admission $6.30 and the cost of adult admission $9.80 and on Wednesday 144 tickets were sold for a total sales of $1124.20.
Let the child tickets are x and adult tickets are y.
On Monday, 144 tickets were sold for a total sales.
x+y=144 ........(1)
Total sales = $1124.20
Need to find the child tickets sold on Wednesday.
Total sales = 6.30x+9.80y
Total sales = $1124.20
So,6.30x+9.80y=1124.20 .......(2)
Find the value of y from equation (1), we get
x+y-x=144-x
y=144-x
Now, we will substitute the value of y in equation (2) to find the value of x, we get
6.30x+9.80(144-x)=1124.20
Apply the distributive property that is a(b+c)=ab+ac, we get
6.30x+9.80×144-9.80x=1124.20
6.30x+1411.2-9.80x=1124.20
Combine the variable terms on left side, we get
1411.2-3.5x=1124.20
subtract 1411.2 from both sides, we get
1411.2-3.5x-1411.2=1124.20-1411.2
-3.5x=-287
Divide both sides with -3.5x, we get
-3.5x/(-3.5)=-287/(-3.5)
x=82
Therefore, 82 child tickets were sold on Wednesday when cost of child admission $6.30 and the cost of adult admission $9.80.
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Direct materials $ 5.50 direct labor $ 3.00 variable manufacturing overhead $ 1.50 fixed manufacturing overhead $ 4.00 fixed selling expense $ 2.50 fixed administrative expense $ 2.00 sales commissions $ 1.00 variable administrative expense $ 0.50 13. if the selling price is $21.50 per unit, what is the contribution margin per unit? (do not round intermediate calculations. round your answer to 2 decimal places.)
The contribution margin per unit is $ 1.50
The contribution margin is the percentage of a product's sales revenue that isn't consumed by variable costs and goes toward paying the firm's fixed expenses.
One of the main components of break-even analysis is the idea of contribution margin.
Labor-intensive businesses with few fixed expenses tend to have low contribution margins, whereas capital-intensive, industrial businesses have more fixed costs and, thus, higher contribution margins.
According to the question,
Total expenses per unit = $(5.50+3.00+1.50+4.00+2.50+2.00+1.00+0.50)
= $ 20
Selling Price per unit = $ 21.50
Thus, contribution margin per unit = $ (21.50 - 20)
= $ 1.50
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K
Use the commutative law of multiplication to write an
14+ ab
equivalent expression.
....
Applying the commutative law to our question, we have; 14 + ab = ab + 14
How to use the commutative law?The commutative law in algebra states that the change in position of two numbers while adding or multiplying them does not change the result. For example;
ab + cd = cd + ab
similarly, fg * jk = jk * fg
Applying the above commutative law to our question, we have;
14 + ab = ab + 14
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In a recent baseball season, Ron was hit by pitches 19 times in 596 plate appearances during the regular season. Assume that the probability that Ron gets hit by a pitch is the same in the playoffs as it is during the regular season. In the first playoff series, Ron has 22 plate appearances. What is the probability that Ron will get hit by a pitch exactly once
The probability that Ron will get by a pitch exactly once is 0.351912.
Given that out of 596 plate appearance Ron was hit 19 times from pitches.
We have to find the probability that ron was hit by pitches in 22 plate appearances.
The value of probability lies between 0 and 1. The formula of calculating proabability is number of items/ total items.
We can find the required probability through binomial distribution which is
n[tex]C_{r}p^{r} (1-p)^{n-r}[/tex] where n is the number of trials and r is the successes.
Probability that Ron will be hit =19/596
=0.031
Probability that Ron will get hit by a pitch exactly once =P(X=1)
=[tex]22C_{1}(0.031)^{1} (1-0.031)^{21}[/tex]
=22!/1!21!*0.031*[tex](0.969)^{21}[/tex]
=22*0.031*0.516
=22*0.015996
=0.351912
Hence the probability that Ron will get hit by a pitch exactly once is 0.35.
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Question 1 (1 point)
m2IJK-570 and mZIJL-20°. Find mZLJK.
3
→K
O a MZLJK-77°
Ob mZLJK-37°
Oc mZLJK-40°
Od mZLJK=-37°
Answer:
37°
Step-by-step explanation:
Subtract angle IJL from angle IJK.
What's the value of this python expression: (2**2) == 4?
Answer:
Python will return:
True
Step-by-step explanation:
The math function ** is an exponent indicator.
The equation you made was:
[tex]2^2 =4[/tex]
When you run this in python, it will return as true.
It is run as a Boolean expression because you have already provided the answer to the expression with the "==" statement.
If you had provided an incorrect answer (setting it equal to any number other than 4), it would return False.
Triangle DEF is congruent to triangle UVW. The length of side DE is 6 cm, EF is 7.5 cm, and DF is 5 cm. What is the length of side VW?
The length of side VW is 7.5 cm
What is the length of side VW?The given parameters are:
DE is 6 cm, EF is 7.5 cm, and DF is 5 cm
Since the two triangles are congruent, then it means that:
D corresponds to UE corresponds to VF corresponds to WSo, we have:
VW= EF
The side EF is
EF = 7.5 cm
So, we have:
VW = 7.5 cm
Hence, the length of side VW is 7.5 cm
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Which is the best estimate of -14 1/9 (-2 9/10) ?
Answer:
42
Step-by-step explanation:
-14 1/9 is about -14.
-2 9/10 is about -3.
Multiplying these, we get (-14)(-3)=42.
. the percentage error if 625.483 is approximated to 3 significant digits is
a. 0.0662
b. 0.0772
c. 0.0552
d. 0.0882
Percentage error is the difference between an actual value and its expected value per the actual value which is expressed in percentage. In the given question, the percentage error is option b. 0.0772
Percentage error is the difference between an actual value and its expected value per the actual value which is expressed in percentage.
This can be expressed as;
percentage error = [tex]\frac{actual value - expected value}{actual value}[/tex] x 100%
Where the actual value is the accurate value, and the expected value is derived from the actual value.
Thus in the given question, it can be deduced that,
actual value = 625.483
expected value = 625.000
The difference between the two values = (625.483 - 625.000)
= 0.483
So that,
percentage error = [tex]\frac{0.483}{625.483}[/tex] x 100%
= 0.07722
percentage error = 0.0772
Therefore, the required percentage error is 0.0772 i.e option b.
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What addition/subtraction equation should I put?
Answer:
7 - 10
Step-by-step explanation:
Because it is -3 and 7 - 10 = -3
Area=
Help me please thanks so much :)
Answer:
48π
Step-by-step explanation:
To find the area of the shaded region, find the area of the large circle and the small circle then subtract.
Large circle:
8²π=64π
Small circle:
4²π=16π
Now subtract 16 from 64.
64-16=48
The area of the shaded region is 48π.
Hope this helps!
which of the following best describes this graph
x² - 4x + 4 is the graphed parabola, so the correct option is D.
Which equation is the graphed one?
On the graph, we can see a parabola that opens upwards (then the leading coefficient is positive), and has a vertex at the point (2, 0).
Also, we can see that the y-intercept is y = 4, that means that the constant term of the parabola is 4.
The only option with a constant term equal to 4 is the last option:
y = (x - 2)*(x - 2) = x² - 4x + 4
So that is the graphed parabola.
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7. Jeff and Stephen go to the mall. The two
boys buy a total of 15 T-shirts. Stephen gets
three less than twice as many T-shirts as Jeff.
a) Write an equation to represent the
information in the second sentence.
b) Write an equation to represent the
information in the third sentence.
c) Solve the linear system by substitution
to find the number of T-shirts each boy
bought.
d) If the T-shirts cost $8.99 each, how
much did each boy spend before taxes?
Answer:
Let j = number of shirts Jeff bought and s = the number of shirts Stephen bought.
a.) s + j = 15
b.) 2j - 3 = s
c.) Plug 2j -3 into the equation from question a.
2j -3 + j = 15
3j -3 = 15
3j = 18
j = 6
2j - 3 = s when j = 6
2(6) - 3 = s
s = 9
Jeff bought 6 shirts; Stephen bought 9 shirts.
d.) Jeff cost = 8.99(6) = $53.94
Stephen cost = 8.99(9) = $80.91
halp pls ok
x =x=x, equals
^\circ
∘
Answer:
60
Step-by-step explanation:
The yellow and green angles form a right angle, so the measures of those combined will be 90 degrees.
90 - 30 = 60
6.6x 10⁵ in standard notation
Answer:
660000
Step-by-step explanation:
WILL MAKE BRAINLIEST!!!
Match each pair of angles to their relationship name (put letters next to the relationship name)
_1. Vertical
_2. Same side interior
_3. Alternate interior
_4. Corresponding
_5. Same-side exterior
_6. Alternate Exterior
_7. Supplementary
_8. No relationship
Answer:
corresponding, supplementary, alternate interior, same side interior, vertical, alternate exterior, corresponding, alternate exterior, vertical, and alternate interior
In the figure 10, the pair of angles are alternate interior angles.
What are angles of parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
From the given figure,
1) corresponding angles
2) Adjacent angles (Supplementary)
3) Alternate interior angles
4) Allied angles (Same side interior)
5) Vertically opposite angles
6) Alternate exterior angles
7) corresponding angles
8) Alternate exterior angles
9) Vertically opposite angles
10) Alternate interior angles
Therefore, in the figure 10, the pair of angles are alternate interior angles.
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The volume of a certain right circular cone is 30 cubic inches. What is the volume, in cubic inches, of a second right circular cone with half the radius and twice the height of the first cone
Answer:
V = 15 in.³
Step-by-step explanation:
The original cylinder has radius r and height h.
V = πr²h
Its volume is 30 in.³, so
πr²h = 30 in.³
The new cylinder has radius (1/2)r and height 2h.
Its volume is
V = π(r/2)²(2h)
V = πr² × 2h/4
V = πr²h/2
πr²h is the volume of the original cylinder, and it is 30 in.³.
V = 30 in.³/2
V = 15 in.³
Jessica purchased a dvd that was on sale for 12% off. the sales tax in her county is 3%. let y represent the original price of the dvd. write an expression that can be used to determine the final cost of the dvd. how do i solve a problem like this ? khan academy
Jessica purchased a DVD that was on sale for 12% off.
The sales tax in her county is 3%.
Let, y represent the original price of the DVD.
We can simply solve this mathematical problem by using the following mathematical process.
Here, we will form an algebraic expression, according to the given data.
So,
The original price of the DVD = y
Discount on the original price :
y * 12/100
=3y/25
Price after discount :
y - 3y/25
=25y - 3y/25
=22y/25
Sales tax amount :
22y/25 * 3/100
11y/25 * 3/50
=33y/1250
Final price including the sales tax :
22y/25 + 33y/1250
1100y + 33y/1250
1133y/1250
(This will be considered as the final result.)
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