The measure of the acute angle is 60 degrees
Trigonometry identityGiven the following trigonometry equation
tan x=2sinx
This can also be written as;
sinx/cosx=2sinx
Simplify to have:
1/cosx =2
2cosx = 1
cosx = 1/2
x = arccos(1/2)
x = 60 degrees
Hence the measure of the acute angle is 60 degrees
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Suppose y varies Inversely with x, and y = -1 when x = 3. What Inverse variation equation relates x and y?
The product of variables in inverse proportion is constant, so the equation is [tex]\boxed{xy=-3}[/tex]
3x+7-6=(8/7)-0
Value of x?
Answer:
[tex]\boxed{\sf x = \dfrac{1}{21}}[/tex]
Explanation:
[tex]\rightarrow \sf 3x+7-6= \dfrac{8}{7} - 0[/tex]
simplify the following
[tex]\rightarrow \sf 3x+1= \dfrac{8}{7}[/tex]
subtract 1 from both sides
[tex]\rightarrow \sf 3x+ 1 -1= \dfrac{8}{7} - 1[/tex]
simplify the following
[tex]\rightarrow \sf 3x= \dfrac{1}{7}[/tex]
multiply both sides by 1/3
[tex]\rightarrow \sf 3x \cdot \dfrac{1}{3}= \dfrac{1}{7}\cdot \dfrac{1}{3}[/tex]
simplify the following
[tex]\rightarrow \sf x = \dfrac{1}{21}[/tex]
[tex]3x + 7 - 6 = \frac{8}{7} - 0 \\ \\ 3x + 1 = \frac{8}{7} \\ \\ 3x = \frac{8}{7} - 1 \\ \\ 3x = \frac{ 8 - 7}{7} \\ \\ 3x = \frac{1}{7} \\ \\ x = \frac{1}{7 \times 3} \\ \\ x = \frac{1}{21} .[/tex]
Please help me
14.7 ÷ 4.2
Answer:
how many times does 4.2 go into 14.7
1. 4.2
2. 8.4
3. 12.6
14.7-12.6=2.1 or one half of 4.2
3.5
Hope This Helps!!!
x^2 - 20x= -2x - 80 what is the intermediate step
Ayuda por favor
Sea ABC un triángulo equilátero de la 2a y altura h
como se muestra en la figura. Si se traza una línea
horizontal que divide la altura del triángulo en dos
partes iguales formando 2 figuras geométricas de
igual altura, entonces el cociente entre el área del
triángulo AMN y el cuadrilátero BMNC es:
A partir de la definición de razón y la teoría de semejanza entre triángulos, la razón del área del triángulo AMN y el área del cuadrilátero BMNC es equivalente a 1/3.
¿Cómo determinar la medida de un lado de un triángulo desconocido?
En este problema tenemos un sistema formado por dos triángulos similares, la semejanza entre los dos triángulos se debe a la colinealidad entre los segmentos de línea AP' (triángulo pequeño) y AP'' (triángulo grande), así como de los lados AM y AB, así como los lados AN y AC, así como los mismos ángulos en la misma distribución. (Semejanza Lado - Ángulo - Lado)
En consecuencia, obtenemos las siguientes proporciones:
AP'/AP'' = MN/BC = 1/2 (1)
Finalmente, la proporción entre el triángulo AMN y el cuadrilátero BMNC es:
[tex]\frac{AMN}{ABC - AMN} = \frac{\frac{1}{2}\cdot a \cdot \left(\frac{1}{2}\cdot h \right)}{\frac{1}{2}\cdot (2\cdot a) \cdot h - \frac{1}{2}\cdot a \cdot \left(\frac{1}{2}\cdot h \right)} = \frac{\frac{1}{4}\cdot a\cdot h }{a\cdot h - \frac{1}{4}\cdot a \cdot h }[/tex]
[tex]\frac{AMN}{ABC - AMN} = \frac{\frac{1}{4} }{\frac{3}{4} } = \frac{1}{3}[/tex]
A partir de la definición de razón y la teoría de semejanza entre triángulos, la razón del área del triángulo AMN y el área del cuadrilátero BMNC es equivalente a 1/3.
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Find f(x) and g(x) so that the
function given can be described
as y = f(g(x)).
Answer:
[tex]g(x) = x^3+1\\f(x) = x^2[/tex]
Step-by-step explanation:
Answer:
f(x)=x^2 and g(x)=x^3+1
Step-by-step explanation:
to find y=f(g(x))
substitute g(x) into f(x)
y= (x^3+1)^2.
If a = 7, b = 2 and c = 3, evaluate: a-bc.
Answer: 1
Step-by-step explanation:
[tex]a-bc=7-2(3)=7-6=\boxed{1}[/tex]
Which of the following is the best buy?
a 6 oz box of rice for $0.90
a 12 oz box of rice for $1.93
a 16 oz bag of rice for $2.42
a 9 oz box of rice $1.25
The best buy is a 9 oz box of rice $1.25. (option d)
What is the best buy?In order to determine the best buy, the unit cost of each option has to be determined. The best buy is the option with the lowest unit cost. The unit cost can be determined by dividing the total cost by the total quantity.
Unit cost = total cost / total oz
$0.90 / 6 = $0.15
$1.93 / 12 = $0.16
$2.42 / 16 = 0.151
$1.25 / 9 = 0.14
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I need this asap. Would appreciate for y’all help
Answer:
-3/2, -1
Step-by-step explanation:
Each coordinate contains one [tex]x[/tex] value and one [tex]y[/tex] value, [tex](x,y)[/tex].
If we work out the midpoint of each of these individually, it makes it much easier to find the midpoint of the line.
Let's take the [tex]x[/tex] values first. Our first [tex]x[/tex] value is -4 and our second [tex]x[/tex] value is 1. Imagine the integers between -4 and 1 laid out in a sequence:
[tex]-4, -3, -2, -1, 0, 1[/tex]
If you take the middle value of this sequence, you get the midpoint of the [tex]x[/tex] values.
In this case, the middle is between values -2 and -1, leaving us with a midpoint of -1.5. This as a fraction is [tex]-\frac{3}{2}[/tex].
Now let's look at the [tex]y[/tex] values. Our first [tex]y[/tex] value is 2 and our second [tex]y[/tex] value is -4. Again, let's imagine those numbers laid out in a sequence:
[tex]2, 1, 0, -1, -2, -3, -4[/tex]
Here, the middle of these values is -1, and this is the midpoint of the [tex]y[/tex] values.
So if we put these two values in a coordinate, we get the midpoint of the line.
In this case, we get [tex](-\frac{3}{2} ,-1)[/tex].
Question 3(Multiple Choice Worth 4 points)
Which expression is equivalent to (7³)-2?
1
7-7-7-7-7-7
07
01
7
-1
7-7-7-7-7-7
frm
Solve the following questions: a. 17 x 10 = b. 24 x 100 = c. 6 x 1000 =
a. 17 x 10 = 170
b. 24 x 100 = 2400
c. 6 x 1000 = 6000
In your job with the heating contractor you photograph houses with infrared film and use the pictures to determine where to place additional installation you need to buy 18 rolls of film a local camera shop sells to film for $9.95 parole plus 5% sale tax mail order company sells to film for $975 parole and charges $15 to ship the whole order but no charges on sales tax if you choose the better of the two prices how much will you pay for 18 rolls of film
Answer:
$188.06
Step-by-step explanation:
The total cost for the film will be the sum of film cost, applicable sales tax, and applicable shipping charges. The film cost will be the product of the number of rolls and the cost per roll.
__
camera shopfilm cost = (18 rolls) × ($9.95 /roll) = $179.10
sales tax = 0.05 × $179.10 = $8.96
There is no shipping charge associated with the camera shop purchase, so the total cost is ...
camera shop cost = film cost + sales tax = $179.10 +8.96 = $188.06
__
mail orderfilm cost = (18 rolls) × ($9.76 /roll) = $175.50
shipping charge = $15.00
There is no sales tax associated with the mail order, so the total cost is ...
mail order cost = film cost + shipping charge = $175.50 +$15.00 = $190.50
__
The price from the camera shop is the better of the two prices. The purchase there would cost you $188.06 for 18 rolls of film.
_____
Additional comment
The after-tax charge per roll of film at the camera shop is 9.95×1.05 = 10.4475. This is $0.6975 more than the basic charge per roll from the mail order company. In order to get the shipping charge of $15 to be less than $0.6975 per roll, the number of rolls ordered must be more than 15/0.6975 = 21.5.
An order of 22 rolls of film from the mail order company would cost less than from the camera shop. ($229.50 vs. $229.85)
if a tv has a diagonal measurement of 55 and a height of 30, what is the tvs width? round to the nearest whole number
Answer:
46
Step-by-step explanation:
The geometry can be modeled by a right triangle. The diagonal measure is the hypotenuse, and the height is one leg. The width is the other leg, and can be found using the Pythagorean theorem.
__
Pythagorean theoremThe relation between the leg lengths (a, b) and the hypotenuse (c) is ...
c² = a² +b²
Solving for b gives ...
b = √(c² -a²)
applicationIn this problem, we have c=55 and a=30. Then the width of the TV is ...
b = √(55² -30²) = √(3025 -900) = √2125
b ≈ 46.098
The width of the TV is about 46.
Help me pleaseeeeeeeeeeeeeeeeeeeeee
Answer:
A
Step-by-step explanation:
[tex]s=\frac{a+b+c}{2}[/tex]
multiply both sides by 2
[tex]2s = a + b +c[/tex]
substract b and c from both sides to get a by itself
[tex]a = 2s - (b + c)\\a = 2s - b - c[/tex]
so the answer is A.
1. What is pi?
2. And why is it important?
Answer:
pi [π] is the ratio of a circle's circumference to its diameter, and it is constant [meaning it is always the case] for all circles.
{this is a long number, 3.141592653589793238... is not even the full length, but 3.14 [or 3.14159] is typically used for estimation}
The significance of pi is typically centered in math--it can be used to find values that we don't know of circles. There are other areas of math that have been related back to the value of pi--which is incredible, and genuinely relevant.
We can find pi in the shape of rivers, physics--including waves--DNA
[+ anywhere there is a circle]
hope this helps!! :)
Answer:
ratio of circle's circumference to diameter
it is constant
Susan has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Susan developed the following table:
The Maximax decision is that Susan should build a very large gas station due to the largest value of row maximums.
What is a decision table?A decision table can be defined as a type of table that is used for the graphical representation of the actions to perform, especially based on given conditions and business level rules.
The decision table for Susan’s problem is shown below:
Size Good market Fair market Poor market Row maximum
Small 50,000 20,000 -10,000 50,000
Medium 80,000 30,000 -20,000 80,000
Large 100,000 30,000 -40,000 100,000
Very large 300,000 25,000 -160,000 300,000
Thus, the Maximax decision is for Susan to build a very large gas station due to the largest value of row maximums.
For the Maximin decision, we have:
Size Good market Fair market Poor market Row minimum
Small 50,000 20,000 -10,000 -10,000
Medium 80,000 30,000 -20,000 -20,000
Large 100,000 30,000 -40,000 -40,000
Very large 300,000 25,000 -160,000 -160,000
Therefore, the Maximin decision is that Susan should build a small gas station due to the largest value of row minimums.
For the equally likely decision, we would find the row average:
Row 1 = (50,000 + 20,000 - 10,000)/3 = 20,000.
Row 2 = (80,000 + 30,000 - 20,000)/3 = 30,000.
Row 3 = (100,000 + 30,000 - 40,000)/3 = 30,000.
Row 4 = (300,000 + 25,000 - 160,000)/3 = 55,000.
Hence, the equally likely decision is that Susan should build a very large gas station due to the largest value of row average.
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Complete Question:
Even though independent gasoline stations have been having a difficult time, Susan has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, Susan developed the following table:
a. Develop a decision table for this problem
b. What is the maximax decision?
c. What is the maximin decision?
d. What is the equally likely decision?
perform the following operation.
-49 - +65 =
Answer:
Step-by-step explanation:-49 - + 65= ?, 65-49 = 16 , so we take 65-49 as normal which is = 16 but it's -16,cuz we were given negative45
Find the value of d.
Answer:
Step-by-step explanation:
Comment
The rule that governs this situation is the average of arc d and 94 = the angle where the chords cross.
Givens
Arc 1 = 94
Arc2 = d
interior angle = 75
Formula
(d + 94)/2 = interior angle/1
Solution
(d + 94)/2 = interior angle/1 Cross Multiply
1*(d + 94) = 75 *2 Combine
d + 94 = 150 Subtract 94 from both sides
d + 94 - 94 = 150 - 94 Combine
d = 56
Answer: d = 56
Consider the given density curve.
A density curve is at y = StartFraction 1 Over 8 EndFraction and goes from negative 10 to negative 2.
What is the value of the median?
–10
–7
–6
–2
Picture posted below…
Answer: -6
Step-by-step explanation:
[tex]\frac{-10-2}{2}=\boxed{-6}[/tex]
The Median of the density is -6.
An illustration of a numerical distribution with continuous results is a density curve. A density curve is, in other words, the graph of a continuous distribution. This implies that density curves can represent continuous quantities like time and weight rather than discrete events like rolling a die (which would be discrete). As seen by the bell-shaped "normal distribution," density curves either lie above or on a horizontal line (one of the most common density curves).
It is clearly visible from the uniform density curve given in the question that the median of the population density is -6.
Because the area to the left and right of the density curve is the same.
Hence, the Median of density is -6.
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C) Three yam tubers are chosen at random from 15 tubers of which 5 are spoilt. Find the probability that, of the three chosen tubers: a) none is spoilt b) all are spoilt c) exactly one is spoilt d) at least one is spoilt.
[tex]\displaystyle\\|\Omega|=\binom{15}{3}=\dfrac{15!}{3!12!}=\dfrac{13\cdot14\cdot15}{2\cdot3}=455[/tex]
a)
[tex]\displaystyle\\|A|=\binom{10}{3}=\dfrac{10!}{3!7!}=\dfrac{8\cdot9\cdot10}{2\cdot3}=120\\\\P(A)=\dfrac{120}{455}=\dfrac{24}{91}\approx26.4\%[/tex]
b)
[tex]\displaystyle\\|A|=\binom{5}{3}=\dfrac{5!}{3!2!}=\dfrac{4\cdot5}{2}=10\\\\P(A)=\dfrac{10}{455}=\dfrac{2}{91}\approx2.2\%[/tex]
c)
[tex]\displaystyle\\|A|=\binom{10}{2}\cdot5=\dfrac{10!}{2!8!}\cdot5=\dfrac{9\cdot10}{2}\cdot5=225\\\\P(A)=\dfrac{225}{455}=\dfrac{45}{91}\approx49.5\%[/tex]
d)
[tex]A[/tex] - at least one is spoilt
[tex]A'[/tex] - none is spoilt
[tex]P(A)=1-P(A')[/tex]
We calculated [tex]P(A')[/tex] in a).
Therefore
[tex]P(A)=1-\dfrac{24}{91}=\dfrac{67}{91}\approx73.6\%[/tex]
A=CD-B how to solve for B
Answer:
Step-by-step explanation:
B=CD-A
If the present value of a growing perpetuity is 214, the required rate of return is 10%, and growth rate is 3%, what is the cash flow in year 1? (Round to the nearest whole number).
The cash flow in year 1 is $15.
What is the cash flow in year 1?A growing perpetuity increases continuously and indefinitely.
Cash flow = present value x (rate of return - growth rate)
214 x (10% - 3%)
214 x 0.07 = $15
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. The probability that a patient catches flu is 3/8, the probability that he has a headache
is 5/15, and the probability that he has asthma is 4/9. If we know the fact that the
probability that the patient will have at least one of the illnesses is 3/5, then what is
the probability that he will have flu, headache, and asthma?
Answer:
[tex]\boxed {\frac{343}{360}}[/tex]
Step-by-step explanation:
Probability Rule :
[tex]\boxed {P(A\cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B \cap C)}[/tex]
Solving :
⇒ 3/5 = 3/8 + 5/15 + 4/9 - P (A ∩ B ∩ C)
⇒ P (A ∩ B ∩ C) = 3/8 + 1/3 + 4/9 - 1/5
⇒ P (A ∩ B ∩ C) = 135/360 + 120/360 + 160/360 - 72/360
⇒ P (A ∩ B ∩ C) = (135 + 120 + 160 - 72) / 360
⇒ P (A ∩ B ∩ C) = 343/360
lexia ran three laps around her neighborhood. Each lap is 1 and StartFraction 3 over 8 EndFraction miles. Which is the best estimate of the number of miles that Alexia ran?
2 miles
3 and one-half miles
4 and one-half miles
6 miles
Answer: The best estimate of the number of miles that Alexia run is 4 miles.
Step-by-step explanation:
Since we have given that
Length of lap is given by
Number of laps around her neighborhood = 3
So, Total number of miles that Alexia ran is given by
Hence, the best estimate of the number of miles that Alexia run is 4 miles
Which of the following points lies on the 2x + 4y =10
Answer:Yes, the point lies on the line.
Step-by-step explanation:
Given coordinate of the locus = (1,2)
Equation of the line 2x+4y = 10
Unknown:
Does the given coordinate lie on the line?
Solution:
The equation given is that of a straight line. To solve this problem, we simply plug the coordinates of the point back into the equation and check if solves it.
x = 1 and y = 2;
2x+4y = 10
So;
2(1) + 4(2) gives 2 + 8 = 10
Yes, the point lies on the line.
Tioga Company manufactures sophisticated lenses and mirrors used in large optical telescopes. The
company is now preparing its annual profit plan. As part of its analysis of the profitability of individual
products, the controller estimates the amount of overhead that should be allocated to the individual product lines from the following information.
Lenses Mirrors
Units produced ................................................................................................................ 25 25
Material moves per product line ........................................................................................ 5 15
Direct-labor hours per unit ................................................................................................ 200 200
The total budgeted material-handling cost is $50,000.
Required:
1. Under a costing system that allocates overhead on the basis of direct-labor hours, the materialhandling costs allocated to one lens would be what amount?
2. Answer the same question as in requirement (1), but for mirrors.
3. Under activity-based costing (ABC), the material-handling costs allocated to one lens would be
what amount? The cost driver for the material-handling activity is the number of material moves.
4. Answer the same question as in requirement (3), but for mirrors.
Tioga Company manufactures sophisticated lenses and mirrors used in large optical telescopes, the values are mathematically given as
MH1=$1,000MH2=$1,000MH3=$1500MH4=$1500What is the material handling costs allocated?Generally, the equation for Material-handling cost for one lens mathematically given as
MH1=Total projected costs for material handling /{Total number of direct labor hours x Direct labor hours per unit)
MH1={$50,000/10.000)x 200
MH1=$1,000
2)
Material-handling cost for one mirror
MH2=Total budgeted material handling cost/ Total number of direct labor hours x direct labor hours per unit
MH2={$50,000/10.000)x 200
MH2=$1,000
3) Material-handling cost per lens
[tex]MH3=\frac{Total projected costs for material handling}{\frac{Number of material moves per lens + Number of material moves per mirror}{(Total number of lenses)}}* Material moves per lens[/tex]
[tex]MH3=\frac{50,000}{\frac{5+15}{25}}*5[/tex]
MH3=$1500
4)
[tex]MH4=\frac{Total projected costs for material handling}{\frac{Number of material moves per mirror + Number of material moves per lens}{(Total number of mirror)}}* Material moves per mirror[/tex]
[tex]MH4=\frac{50,000}{\frac{5+15}{25}}*5[/tex]
MH4=$1500
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4/3 - 1/2 What is the answer
Answer:
5/6
Step-by-step explanation:
4/3-1/2
1) make the denominators the same on both fractions
8/6-3/6=?
2) subtract numerators
5/6
3) simplify
cannot simplify
Answer:
5/6
Step-by-step explanation:
4/3 -1/2
The first step is to get a common denominator of 6
4/3 *2/2 = 8/6
1/2 * 3/3 = 3/6
8/6 -3/6
5/6
Please help I’m confused
Answer:
Step-by-step explanation:
(08.01 MC)
Find the height of a square pyramid that has a volume of 75 cubic feet and a base length of 5 feet.
A. 5 feet
B. 9 feet
C. 25 feet
D. 45 feet
Answer:
A. 5 feet
Step-by-step explanation:
Multiply (3a³-6b³) (4a² + 5b²)
Answer:
[tex]12a^5+15a^3b^2-24b^3a^2-30b^5[/tex]
Step-by-step explanation:
(3a³-6b³) (4a² + 5b²) -> Simplify not Multiply
Expand (3a³-6b³) (4a² + 5b²) using the FOIL Method.
Apply the distributive property.
[tex]3a^3(4a^2+5b^2)-6b^3(4a^2+5b^2)[/tex]
[tex]3a^3(4a^2)+3a^3(5b^2)-6b^3(4a^2+5b^2)[/tex]
[tex]3a^3(4a^2)+3a^3(5b^2)-6b^3(4a^2)-6b^3(5b^2)[/tex]
Simplify each term.
Rewrite using the commutative property of multiplication.
[tex]3*4a^3a^2+3a^3(5b^2)-6b^3(4a^2)-6b^3(5b^2)[/tex]
↓
[tex]12a^5+15a^3b^2-24b^3a^2-30b^5[/tex]
Equation Simplified.
---------------------------------------------------------------------------------------
Hope this helped!