Answer:
n = 89Step-by-step explanation:
Use of identitiestan (x - y) = (tan x - tan y)/(tan x tan y + 1) 1/tan x = cot xtan (90 - x) = cot xtan (- x) = - tan xConvert the first one above:
tan x tan y = (tan x - tan y) / tan (x - y) - 1Apply this to each term of the given expression to get:
tan1°tan2° + tan2°tan3° + ... + tan88°tan89° = (tan1° - tan2°)/(tan-1°) - 1 + (tan2° - tan3°)/(tan-1°) - 1 + ... + (tan88° - tan89°)/(tan-1°) - 1 = (tan1° - tan2° + tan2° - tan3° + ... + tan88° - tan89°)/(tan-1°) - 88 = (tan1° - tan89°)/(tan-1°) - 88 = tan1°/ (tan-1°) - tan89°/tan-1° - 88 = - 1 - cot1*(- cot1°) - 88 = cot² 1° - 89The value of n is 89.
Answer:
n = 89
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Tan double angle identity}\\\\$\tan (A - B)=\dfrac{\tan A - \tan B}{1 + \tan A \tan B}$\\\end{minipage}}[/tex]
Rewrite the tan double angle identity to isolate tanAtanB:
[tex]\implies 1 +\tan A \tan B=\dfrac{\tan A- \tan B}{\tan (A - B)}[/tex]
[tex]\implies \tan A \tan B=\dfrac{\tan A- \tan B}{\tan (A - B)}-1[/tex]
Therefore:
[tex]\implies \tan 1^{\circ} \tan 2^{\circ}+\tan2^{\circ}\tan3^{\circ}+...+\tan88^{\circ}\tan89^{\circ}[/tex]
[tex]\implies \left(\dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (1 - 2)^{\circ}}-1\right)+\left(\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (2 - 3)^{\circ}}-1\right)+...+\left(\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (88 - 89)^{\circ}}-1\right)[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (-1)^{\circ}}-1+\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (-1)^{\circ}}-1+...+\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-1[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (-1)^{\circ}}+\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (-1)^{\circ}}+...+\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}+\tan 2^{\circ}- \tan 3^{\circ}+...+\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}}{\tan (-1)^{\circ}}-\dfrac{ \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{ \tan(-x)=-\tan(x)}:[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}}{-\tan 1^{\circ}}+\dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-88[/tex]
[tex]\implies -1+\dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-88[/tex]
[tex]\implies \dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-89[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{\tan(90-x)=\cot(x)}:[/tex]
[tex]\implies \dfrac{\cot1^{\circ}}{\tan1^{\circ}}-89[/tex]
[tex]\implies \cot 1^{\circ} \cdot \dfrac{1}{\tan1^{\circ}}-89[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{\dfrac{1}{\tan(x)}=\cot(x)}:[/tex]
[tex]\implies \cot 1^{\circ} \cdot \cot 1^{\circ}-89[/tex]
[tex]\implies \cot^21^{\circ}-89[/tex]
Therefore, n = 89.
What is the constant rate of change of the table below?
If Jake can type approximately 25 words per minute, how long will it take him to type a 1,000 word paper
Answer
It'll take Jake 40 minutes to type the 1,000 word paper.
Explanation
Working at that same speed, let the number of minutes it will take Jake to type 1,000 word paper be x minutes.
25 words = 1 minute
1,000 words = x minutes
We can write a mathematical relationship for this by cross mutiplying
(25) (x) = (1,000) (1)
25x = 1,000
Divide both sides by 25
(25x/25) = (1,000/25)
x = 40 minutes
Hope this Helps!!!
HELP!! // Your parents allow you to have Internet access on your cell phone as long as you prepay the bill. If your bill is $19.60 per week, how much would you have to save per day to pay the bill? Describe the process you use to solve the problem.
Answer: $2.80 a day
Step-by-step explanation:
you would need to save at least $2.80 a day, just take the total (19.60) and divide it by the number of days you have till its due, in this case a week (7 days) than divide. 19.20/7= 2.8
Is 1/1 a terminating or repeating decimal
6. A large community college has professors
and lecturers. The total number of faculty
members is 228. The school reported that
they had 5 professors for every 14 lecturers.
How many of each type of faculty member™
does the community college employ?
The College employee in total count will be 60 professors and 168 lecturers in the college community.
As given total number of faculty member in the school is 228.
Also we have information that for every 14 lecturers the college community has 5 professors counting ratio.
∴ Let's Combine the number of professor and number of lecturers and make one group as a set.
∴ Total of one set will be 5 + 14 = 19.
Now as we have total 228 members and we have the set value as 19 so we can find the total number of set that can be possible with the given members as follows [tex] \frac{228}{19} = 12 [/tex]
Hence total number of set will be 12.
As one set contains 5 number of professors so 12 sets will contain in total ( 12 * 5 ) = 60 number of professors.
As one set contains 14 number of lecturers so 12 sets will contain in total ( 12 * 14 ) = 168 number of lecturers .
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a car has a15 gallon gas tank and gets a maximum average mileage of 24 miles per gallon
Answer:
360 miles
Step-by-step explanation:
24*15=360
360 miles can be driven in 15 gallons gas.
what is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For, example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
A car has a15 gallon gas tank.
Now, per gallon = 24 miles driven
So, in 15 gallons, the miles driven
= 24 x 15
= 360 miles.
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The figure shows rectangle RSTW. Which of the following conditions satisfies the criteria for rectangles?
i cant upload image
a. m∠SRZ = 40°
b. m∠STZ = 40°
c. m∠SRW = 80°
d. m∠TWR = 80
The condition that satisfies the criteria for rectangles is
m∠SRZ=40°. Option A
This is further explained below.
What is the condition?Generally, The diagram illustrates the rectangle RSTW, which contains the angle RTW with a measurement of forty degrees.
1. The sides SR and TW are perpendicular to one another as opposed sides of the rectangle. Next, the angles SRZ and RTW are alternative inner angles. The alternative inner angles theorem states that because they are congruent, mSRZ must equal 40 degrees. This option should be selected.
2. The angles STZ and RTW are complimentary to one another (they sum up to 90 degrees), and then
m∠STZ=90°-40°=50°. This choice is not a valid option.
3. The SRW angle represents a right angle (in a rectangle all angles are right angles). According to the textbook definition of a right angle,
m∠SRW=90°. This choice is not a valid option.
4. Angle TWR is a right angle (in a rectangle all angles are right angles). According to the textbook definition of a right angle,
m∠TWR=90°. This choice is not a valid option.
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CQ attached
(1 + 2)3 ÷ (2 + 1) =
Answer:
3
The answer is three cuase I did the math but it's hard to explain on here
Help me because i forgot everything :(
The graph that results from placing the coordinates on the graph is shown below.
Consequently, the graph's coordinates are (-1,1), (0,3), and (1,5)
How to solve linear equations on a graph?We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found. The point where the two lines join is (-3, -4), which is where this equation system's solution lies.
There are 3 methods for graphing a linear equation:
1.displaying the graph of a linear equation using two points.
2.Use a linear equation's slope and y-intercept.
3.using a linear equation's x- and y-intercepts.
So we take 3 values to substitute in place of x like
-1,0,1
values of y we get are
1,3,5
Now placing the co ordinates on the graph we get the following graph,
Therefore, the co-ordinates constituting the graph are (-1,1), (0,3), (1,5)
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What is the complete factorization of
-12 + 3x + 28?
F. (x-4)(x-7)
G. -(x-4)(x + 7)
H. -(x + 4)(x + 7)
J. -(x-7)(x + 4)
Answer:
J. - (x-7)(x + 4)
Step-by-step explanation:
There is a proportional relationship between gallons and pints.
A) What is the constant of proportionality to convert gallons to pints? Show your work and/or explain your reasoning.
explain pls
The constant of proportionality to convert gallons to pints given the information in the table is 8.
What is the constant of proportionality?The constant of proportionality is the ratio that equates to variables in a directly proportional relationship. A directly proportional relationship is a relationship where the two variables move in the same direction.
The equation for direct proportionality:
y = bx
where:
y = dependent variable = gallons b = constant of proportionalityx = independent variable = pints16 = 2b
b = 16/2 = 8
40 = 5b
b = 40 / 5 = 8
56 = 7b
b = 56 / 7 = 8
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Find the area of a circle with diameter of 8cm use the value 3.14 for pie and do not round awnser
The area of a circle with a radius r is given by the following formula:
[tex]A=\pi\cdot r^2[/tex]In this case we know that the diameter is 8cm which means that its radius is 4cm. Using 3.14 for pie we get:
[tex]\begin{gathered} A=3.14\cdot(4cm)^2 \\ A=3.14\cdot16cm^2=50.24cm^2 \end{gathered}[/tex]AnswerThen the answer is 50.24 cm².
simplify the expression -1/2 + 1/6
The solution to the fraction -1/2 + 1/6 is -1/3
How to simplify the expression?The expression is given as
-1/2 + 1/6
Rewrite the terms of the expression as equivalent fractions
So, we have the following equation
-1/2 + 1/6 = -3/6 + 1/6
Take the LCM of the equation
So, we have the following equation
-1/2 + 1/6 = (-3 + 1)/6
Evaluate the sum
So, we have the following equation
-1/2 + 1/6 = -2/6
Simplify the quotient
-1/2 + 1/6 = -1/3
Hence, the value of the fraction is -1/3
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Given: GHIJ is a parallelogram.
HP = JQ PQ bisects GI
Prove: PX = QX
Hint: Use subtraction of the side lengths.
PX ≅ QX, as ΔGXP ≅ ΔIXQ is congruent by the AAS property.
Given, GHIJ is a parallelogram.
Given, HP ≅ JQ
GH ≅ JI, as both are on opposite sides it is a congruency property.
GP ≅ QI, the definition of congruency.
GP + PH ≅ JQ + QI, segment addition property.
∡PXG ≅ ∡ IXQ, vertical angles are congruent.
GH || JI, opposite sides are parallel
∠ PGH ≅ ∠QIX, alternate interior angles
PX ≅ QX, corresponding parts of congruent triangles are congruent.
ΔGXP ≅ ΔIXQ is congruent by the AAS property.
Therefore, PX ≅ QX
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What is the slope of the line that passes through the points (10, 4) and (7, 3)?
Answer:
1/3
Step-by-step explanation:
You want to know the slope of the line through points (10, 4) and (7, 3).
Slope formulaThe slope of the line through two points (x1, y1) and (x2, y2) is given by the formula ...
m = (y2 -y1)/(x2 -x1)
ApplicationFor the given points, the slope is ...
m = (3 -4)/(7 -10) = -1/-3 = 1/3
The slope of the line is 1/3.
what is the mean of 45,68,77,90,90,95,100,100,86,90,50,55
Answer:
78.8
Step-by-step explanation:
among all the computer chips produced by a certain factory, 6 percent are defective. a sample of 400 chips is selected for inspection. (a) what is the probability that this sample contains between 20 and 25 defective chips (including 20 and 25)? (b) suppose that each of 40 inspectors collects a sample of 400 chips. what is the prob- ability that at least 8 inspectors will find between 20 and 25 defective chips in their samples?
The number of ways to select a sample of 2 computer chips so that at least one of the chips is defective is 9876 ways.
The box contains 400 computer chips. Of these 400 chips 24 are defective and 376 are good.
A quality control inspector samples 2 computer chips.
The number of ways to select at least 8 defective chip is:
n (At least 8 defective chip) = n (1 defective chip) + n (2 defective chips)+n (3 defective chips)+n (4 defective chips)+n (5 defective chips)+n (6 defective chips)+n (7 defective chips)+n (8 defective chips)
The number of ways to select 1 defective chip is:24C1*400C1=24*400=9600 ways.
The number of ways to select 2 defective chips is: 24C2*400C0=276*1=276ways.
n (At least 1 defective chip) = n (1 defective chip) + n (2 defective chips)
= 9600+276
= 9876
Thus, the number of ways to select a sample of 2 computer chips so that at least one of the chips is defective is 9876 ways.
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9 Write the double that you would use to solve the problem Then solve it. Write your answers in the blanks. 4+5= ? Use the double 4+5=
Please Solve this Algebraic Proof for Geometry!!
2 images attached
The value of x from the given figure is 3. Hence, proved.
Given that, ∠XVW=∠W.
What is vertical angles theorem?When two lines cross at a point, vertical angles are created. They are always on an equal footing. In other words, four angles are created anytime two lines cross or intersect. It is evident that two opposed angles are equal and are referred to as vertical angles. They are also known as "Vertically opposite angles" due to the fact that they are perpendicular to one another.
∠XVW = ∠W (Given)
∠XVW = ∠ZVY (Vertical angles theorem, vertical angles are congruent.)
∠ZVY = ∠W (Transitive property of congruence)
m ∠ZVY = m ∠W (Angle congruence postulate)
8x+13=75x+28 (Substitution property of equality)
5x=15 (Subtraction property of equality)
x=3 (Division property of equality)
The value of x from the given figure is 3. Hence, proved.
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help me i don’t understand
Answer:
23cm
Step-by-step explanation:
in this case, you don't have to actually care both the 4 because it is not a side. whoever did that is trying to trick you. now you are left with 7cm,6cm, and 10cm.
10+6+7=23
Write the time in the blank below
Answer: 6:30
Step-by-step explanation: every number you count by 5 and the short hand is the hour hand.
explain the strategy you used to sove this equation 3(5x-2)=3x+8-2x
Answer:
x = 1
Step-by-step explanation:
3(5x-2)=3x+8-2x
Apply the Distributive Property
15x - 6 3x+8 - 2x
Combine like terms
15x-6= x+8
Rearrange variables to the left side of the equation
15x-x=8+6
Combine like terms
14x 8+6
(I don't know if you want me to answer it)
Use the marginal tax rate chart to answer the question.
Determine the amount of taxes owed on a taxable income of $49,652.
•$4,735.38
•$6,600.44
•$7,709.92
•$10,293.44
The amount of taxes owed on a taxable income of $49,652 is 10,293.44.
what is Marginal tax rate?The amount of additional tax paid for each new dollar of income received is known as the marginal tax rate. Total taxes paid divided by total income earned is the average tax rate. With a marginal tax rate of 10%, tax would be deducted from the following dollar of income at a rate of 10%.
For instance, if a person has a taxable income of $24,750, they will pay taxes on the first $19,900 of that income at a rate of 10%, and on the remaining $5,000 at a rate of 12%.
Given:
Income= $49652
The above amount lies in the range of 41176- 89075 which has tax rate pf 22%.
So, the amount of taxes
= 49652 x 22%
=49652 x 22/100
= 49652 x 0.22
= 10,293.44
Hence, the amount of taxes owed on a taxable income of $49,652 is 10,293.44.
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Answer:
$6,600.44
Step-by-step explanation:
$49,652 falls into the 22% bracket.
Basically you take the taxable amount from each bracket and then multiply each by the corresponding marginal tax rate.
Then we take the income $49,652 and subtract it by the maximum of the last tax bracket which would be $41,175.
$49,652 - $41,175 = $8,477.
Multiply this by 22% = 1,864.94 then add the other brackets' taxes owed which should total to $6,600.44
the healthcare provider prescribes propofol (diprivan) at 8 mcg/kg/minute for a client during conscious sedation. the drug is dispensed as a econdary infusion labled, 0.9% normal saline 50 ml with propofol 100 mg/50 ml the client's weight is 198 pounds. the nurse should program the infusion pump to deliver how many ml/hour? (enter numeric value only. if rounding is required, round to the nearest tenth.)
The nurse should program the infusion pump to deliver 21.6ml/hour
Given the following:
Drug propofol prescribed is 8mcg/kg/min
Drug dispensed in 100mg in 50ml NS
Weight of patient is 198 pounds
Converting pounds in Kg:
198 pounds is (1 pound is 0.45Kg)
89.8 equivalent to 90Kg
Converting 8mcg/kg/min into mg/kg/min:
8mcg is 0.008mg so it becomes 0.008mg/kg/min
Patient weight is 90 kg , so required drug is:
90x0.008=0.72 mg/min
Now 50ml has 100mg, so 1ml has 2mg
We want to give 0.72mg, so if there is 2mg in 1 ml how much will be 0.72 mg for, by doing cross multiplication we get as below:
2mg in 1 ml
0.72=?
=0.72x1/2
=0.36ml
Now we have to give 0.36ml/min
Infusion pump has rate in ml/ hour, as 1 hour has 60 min, we multiply 0.36x60=21.6ml/hour
Hence, Infusion pump delivered 21.6ml/hour
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Select the equation that has the same solution.
brainiest for the best answer. 100 points.
Answer: 11/4n + 2 = -3 +3/2n
Step-by-step explanation:
1) Solve the given equation
-5n + 31 = -14n -5
9n = -36 (Move like terms)
n = -4
2) Solve every other equation until match
1a)
11/4n + 2 = -3 +3/2n
11/4n = -5 + 6/4n (Change fraction and move like terms)
5/4n = -5 (minus fraction)
n = -4 Correct
Using the quadratic formula, find the roots of the equation 3x = 2x² + 1.
A
x = -0.5 and x = −1
B x= 1.5 and x = 0
C
D
x = 2 and x = 1
x = 1 and x = 0.5
Using the quadratic formula we can conclude that the equation 3x = 2x² + 1 has two real roots which are x = 1 and x = 0.5.
What is the quadratic formula?The definition of a quadratic as a second-degree polynomial equation implies that at least one squared term must be present. It also goes by the name quadratic equations. The quadratic equation has the general form ax² + bx + c = 0.The quadratic formula: [tex]x = \frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]
Equation is 3x = 2x² + 1.Then, 2x² -3x + 1.Now, a = 2, b = -3 and c = 1.There are two real roots which are x = 1 and x = 0.5.
(Refer to the image attached below for the working)
Therefore, using the quadratic formula we can conclude that the equation 3x = 2x² + 1 has two real roots which are x = 1 and x = 0.5.
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A lorry travels at a speed of 45 km/h for 2 hours from factory P to factory Q. Then the lorry takes 30 minutes more for its return journey. Calculate the average speed.
40 Km/h will be the average speed of the lorry for the overall journey from factory P to Q and again from factory Q to P.
The distance between the factories can be calculated by the Speed-Time relation.
Total Distance = Total Speed x Total Time = 45Km x 2 = 90Km
To calculate the Average Speed, Total Distance and Total Time are the essential parameters.
Total Distance = 90 + 90 = 180Km
Total Time = 2 + 2.5 = 4.5h
As per the formula of Average speed:
Average speed = Total Distance/ Total Time
Average speed = 90+90Km / 4.5h
= 40Km/h
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On a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level. She notices a sea turtle above her and rises 6 ft to take its picture. At what elevation does the diver take the picture?
The elevation at which the diver takes the picture is -14 3/4 feet if, on a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
On a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level.
Let x be the elevation at which the diver takes the picture.
The value of x can be found as follows:
x = -20 3/4 + 6
x = -83/4 + 6
x = (-83 + 24)/6
x = -59/6
Or
x = -14 3/4 feet
Thus, the elevation at which the diver takes the picture is -14 3/4 feet if, on a cave dive in Oahu, a scuba diver swims at an elevation of 20 3/4 ft relative to sea level.
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Find the equation of the line and passing through (4,3) with slope= -5
The required equation of the line is 5x + y + 17 = 0.
What is an equation?
An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. Equations are used to describe geometric shapes in Cartesian geometry. Because the equations under consideration, such as implicit equations or parametric equations, contain an unlimited number of solutions, the goal has shifted: instead of directly stating the solutions or counting them, which is impossible, one utilizes equations to investigate the features of figures. This is the fundamental concept of algebraic geometry, a significant branch of mathematics. An equation consists of two expressions joined by an equals sign ("="). The expressions on each side of the equals sign are referred to as the equation's "left-hand side" and "right-hand side."
The equation of the line is given below:
y - 3 = -5(x - 4)
or, y - 3 = -5x - 20
or, 5x + y + 17 = 0
Hence, the required equation of the line is 5x + y + 17 = 0.
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60% of a number is 66. Which proportion best represents this relationship?
Responses
66b =60100
Answer:
then answer is never going to give you up never going to let you down