Answers
Answer:
1
Step-by-step explanation:
Cosine is a trigonometric function that is represented by adjacent divided by the hypotenuse. The side adjacent to angle A is AC and the hypotenuse is AB, so we can say cos(A) = [tex]\frac{AC}{AB}[/tex]. We can do the same for angle B. The side adjacent to it is BC, and the hypotenuse is again AB. So, we can say
cos(B) = [tex]\frac{BC}{AB}[/tex]. We are solving for [tex]\frac{cosA}{cosB}[/tex], so we can substitute the value of those two and solve:
[tex]\frac{\frac{AC}{AB}}{\frac{BC}{AB} }[/tex]
[tex]\frac{AC}{AB} * \frac{AB}{BC} = \frac{AC}{BC}[/tex]
AC is given to be 3 and BC is also 3, so [tex]\frac{AC}{BC}[/tex] is [tex]\frac{3}{3}[/tex] which is just 1.
Related Questions
A rope is 56 in length and must be cut into two pieces. If one piece must be six times as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary.
Answers
Answer:
48, 6
Step-by-step explanation:
The ratio of the pieces is 6 to 1
Add them together to get the total
6+1 = 7
Divide the total length by 7
56/7 = 8
Multiply the ratios by 8
6*8 = 48
1*8 = 6
The peices are 48 and 6
A right triangle has one leg that measures 7 inches and the hypotenuse measures 12 inches.
What is the length of the other leg?
Round your answer to the nearest hundredth.
Answer with a numeric value only. That is, do not include "in" or "inches" with your response.
Answers
Using Pythagorean theorem
[tex]\boxed{\sf B^2=H^2-P^2}[/tex]
[tex] \\ \sf \longmapsto \: b = \sqrt{ {h}^{2} - {p}^{2} } \\ \\ \sf \longmapsto \: b = \sqrt{ {12}^{2} - {7}^{2} } \\ \\ \sf \longmapsto \: b = \sqrt{100 - 49} \\ \\ \sf \longmapsto \: b = \sqrt{51} \\ \\ \sf \longmapsto \: b = 7.2in[/tex]
If 800g of a radioactive substance are present initially and 8 years later only 450g remain, how much of the substance will be present after 16 years? (Round answer to a whole number)
Answers
A=Pe^(rt)
P = 800g
t = 8 years
A = 450g
r = This is what we will try and find to start with
450=800e^(r*8)
After running the math through a calculator, we end with r = -0.07192
Now we just re-input this information into our equation: A=800e^(-0.07192*16)
A=800e^(1.15072)
Now we will re-write the equation using the negative exponent rule:
A = 800 1/e^1.15072
Combine right side:
A = 800/e^1.15072
Then do the math:
A = 253.12709836......
That will give us A = 253 (rounded to the whole number)
I hope this helps! :)
The substance that should be presented after 16 years is 253.
Given that,
If 800g of a radioactive substance are present initially and 8 years later only 450g remain.Based on the above information, the calculation is as follows:
We know that
[tex]A=Pe^{rt}[/tex]
Here
P = 800g
t = 8 years
A = 450g
[tex]450=800e^{r\times 8}\\\\A=800e^{-0.07192\times 16}\\\\A=800e^{1.15072}\\\\A = 800 \ 1 \div e^{1.15072}\\\\A = 800\div e^{1.15072}[/tex]
A = 253
Therefore we can conclude that the substance that should be presented after 16 years is 253.
Learn more: brainly.com/question/16115373
what is the value of tan 0 in the unit circle below
Answers
Tangent = opposite / adjacent, or in this case Tangent = y / x.
Tan = (1/2) / ([tex]\sqrt{3}[/tex] / 2)
1 / [tex]\sqrt{3}[/tex]
[tex]\sqrt{3}[/tex] / 3
Hope this helps!
find the value of g-¹(-2) if g (x) =4-2x
Answers
Answer:
Solution given:
g-¹(-2)=?
we have
g(x)=4-2x
let
g(x)=y
y=4-2x
Interchanging role of x and y
x=4-2y
2y=4-x
dividing both side by 2
2y/2=(4-x)/2
y=(4-x)/2
f-¹(x)=(4-x)/2
now
Substitute value -2 in place of x
f-¹(-2)=(4-(-2))/2=(4+2)/2=6/2=3
the value of g-¹(-2) is 3.
Game consoles: A poll surveyed 341 video gamers, and 95 of them said that they prefer playing games on a console, rather than a computer or hand-held device. An executive at a game console manufacturing company claims that the proportion of gamers who prefer consoles differs from . Does the poll provide convincing evidence that the claim is true
Answers
Answer:
proportion of gamers who prefer console does not differ from 29%
Step-by-step explanation:
Given :
n = 341 ; x = 95 ; Phat = x / n = 95/341 = 0.279
H0 : p = 0.29
H1 : p ≠ 0.29
The test statistic :
T = (phat - p) ÷ √[(p(1 - p)) / n]
T = (0.279 - 0.29) ÷ √[(0.29(1 - 0.29)) / 341]
T = (-0.011) ÷ √[(0.29 * 0.71) / 341]
T = -0.011 ÷ 0.0245725
T = - 0.4476532
Using the Pvalue calculator from test statistic score :
df = 341 - 1 = 340
Pvalue(-0.447, 340) ; two tailed = 0.654
At α = 0.01
Pvalue > α ; We fail to reject the null and conclude that there is no significant evidence that proportion of gamers who prefer console differs from 29%
If a hypothesis is not rejected at a 5% level of significance, it _____.
a. will also not be rejected at the 1% level
b. may be rejected or not rejected at the 1% level
c. will always be rejected at the 1% level
d. will sometimes be rejected at the 1% level
Answers
Answer:
a. will also not be rejected at the 1% level.
Step-by-step explanation:
A hypothesis is rejected if:
The p-value is larger than the significance level.
Hypothesis is not rejected at a 5% level of significance
This means that the p-value is > 0.05.
At the 1% level:
p-value > 0.01, so it will never be rejected, and thus, the correct answer is given by option a.
What’s the equation?
Answers
Answer:
The answer is D.
Step-by-step explanation:
If the recipe takes 60 minutes to cook at a temperature of 350 degrees, how many minutes would it take at 200degrees
Answers
Answer:
The temperature has to be inversely proportional to the time therefore the solution will be:
60minutes/200degrees=x/350degrees
200x/200=21000/200
x=105minutes
I hope this helps
Answer:
105 minutes.
Step-by-step explanation:
As 200 degrees is less than 350 it will take longer at 200.
By proportion that would be (350/200) * 60
= 60 * 7/4
= 105 minutes.
If all possible random samples of size N are drawn from a population with a mean of mu and a standard deviation of sigma, then as N becomes larger, the sampling distribution of sample means becomes approximately normal with a mean of muy(bar) and a standard deviation of sigmay(bar). This statement is known as the:
Answers
Answer:
"Central limit theorem" is the right answer.
Step-by-step explanation:
A hypothesis essentially claims that whenever there seems to be a small variance throughout the big confidence intervals, the sampling is based on averages as well as the sampling distribution (mean) usually nearly the same as the public's median.
When,
Mean = [tex]\mu_y[/tex]Standard deviation = [tex]\sigma_y[/tex]Sample size = Nis sufficiently larger than [tex]\bar Y \sim N(\mu_y, \sigma_y)[/tex]
Thus, the above is the right answer.
Please help on this initial amount problem
Answers
Growth
Value of car change 28% each year
How would yo expand ln (1/49k)?
Answers
Answer:
Step-by-step explanation:
It depends on whether you mean ln(1/49k) or ln(1/(49k)).
The following data represents the age of 30 lottery winners.
22 30 30 35 36 37 37
37 39 39 41 51 51 54
54 55 57 57 58 58 61
64 68 69 72 74 75 78 79 80
Complete the frequency distribution for the data.
Age Frequency
20-29
30-39
40-49
50-59
60-69
70-79
80-89
Answers
20-29 ==> 1
30-39 ==> 9
40-49 ==> 1
50-59 ==> 9
60-69 ==> 4
70-79 ==> 5
80-89 ==> 1
(Total 30)
Help solve problem please
Answers
Answer:
1 / 13
Step-by-step explanation:
The total number of cards in a deck = 52
The total number of aces in a deck = 4
Since selection is drawn with replacement, then probability of drawing a certiaj number of card from the deck will be the same each time a selection is made :
Probability = required outcome / Total possible outcomes
The required outcome = number of aces = 4
Total possible outcomes = total number of cards = 52
P(drawing an ace) = 4 / 52 = 1 /13
find x in this similar triangles
Answers
Answer:
6. x = 4
8. x = 13
Step-by-step explanation:
Using similar triangles theorem,
6. (5+4)/5 = (4x + 2)/(4x + 2 - 8)
9/5 = (4x + 2)/(4x - 6)
Cross multiply
9(4x - 6) = 5(4x + 2)
36x - 54 = 20x + 10
Collect like terms
36x - 20x = 54 + 10
16x = 64
16x/16 = 64/16
x = 4
8. (4x + 13)/20 = 52/16
(4x + 13)/20 = 13/4
Cross multiply
4(4x + 13) = 13(20)
16x + 52 = 260
16x = 260 - 52
16x = 208
x = 208/16
x = 13
cho A là ma trận vuông cấp 2 và detA=11, Khi đó det(3A)=
Answers
A problem is given to three students A,B and C whose chances of solving 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?
Answers
Answer:
because
1/2+1/3+1/4
1/2x6+1/3x4+1/4x3
1/12+1/12+1/12
1+1+1/12
3/12
1/4
1:4 so,their is a proability that the problem will be solved.
help asap, will give brainliest. dont answer if u are not 100% sure thank you.
Answers
Answer:
[tex]f(x)=\sqrt[3]{x+11}[/tex]
[tex]y=\sqrt[3]{x+11}[/tex]
[tex](y)^3=(\sqrt[3]{x+11} )^3[/tex]
[tex]y^3=x-11[/tex]
[tex]x=y^3-11[/tex]
[tex]f^{-1} (x)=x^3-11[/tex]
OAmalOHopeO
Jean threw a disc in the air. The height of the disc can be modelled by the function
h = -5t^2 + 31.5t + 2, where h is the height in metres after t seconds.
Patrick fired a paintball at the disc. The path of the paintball is modelled by the function h = 30t + 1, with the same units. How long will it take the paint ball to hit the disc?
Answers
Answer:
It will take 0.62 seconds for the paint ball to hit the disc.
Step-by-step explanation:
Height of the disk:
[tex]H_d = -5t^2 + 31.5t + 2[/tex]
Height of the paintball:
[tex]H_p = 30t + 1[/tex]
When the paintball will hit the disk?
When they are at the same height, so:
[tex]H_d = H_p[/tex]
[tex]-5t^2 + 31.5t + 2 = 30t + 1[/tex]
[tex]5t^2 - 1.5t - 1 = 0[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
In this question:
Quadratic equation with [tex]a = 5, b = -1.5, c = -1[/tex]
So
[tex]\Delta = (-1.5)^2 - 4(5)(-1) = 22.25[/tex]
[tex]t_{1} = \frac{-(-1.5) + \sqrt{22.25}}{2(5)} = 0.62[/tex]
[tex]t_{2} = \frac{-(-1.5) - \sqrt{22.25}}{2(5)} = -0.32[/tex]
Time is a positive measure, so 0.62.
It will take 0.62 seconds for the paint ball to hit the disc.
what’s the missing side of the polygons
Answers
Answer:
the missing side is 21!!!!!!!!
PLEASE HELP I REALLY NEED THIS
How is an inequality different from an equation?
What are four ways inequality can be written?
What would the graph of each inequality look like on a number line? (use an example)
What would the graph of an equation look like on a number line(use an example)
Pam has 15 candies in a jar, her sister threw in some more ( the ones she doesn’t like) and now Pam has 27. Write an equation to determine how many candies ( x) her sister put in the jar. Solve using both inverse operations and a balance scale.
Explain the Golden Rule for solving equations
using an example.
What does it mean if a situation has a condition or constraint? Give an example.
Give an example of a situation that contains an independent and dependent variable. Explain if your data is continuous or discrete.
Answers
Answer:
inequality is mostly represented on a number line but equation is not.
Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height 5h. Use cylindrical shells to compute the volume V of a napkin ring of height 5 h created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h .
Answers
Answer:
V = 1/6 π ( 5h)^3
Step-by-step explanation:
Height of napkin rings = 5h
Compute the volume V of a napkin ring
let a = 5
radius = r
express answer in terms of h
attached below is the detailed solution
Rate of change or rate of change
A farmer has 80 feet of wire mesh to surround a rectangular pen.
A) Express the area A of the pen as a function of x, also draw the figure of A indicating the admissible values of x for this problem.
B) What are the dimensions of the maximum area pen?
Answers
Answer:
Step-by-step explanation:
A). Let the dimensions of the rectangular pen are,
Length = l
Width = x
Since, farmer has the wire measuring 80 feet to surround the the pen.
Perimeter of the pen = 80 feet
2(l + x) = 80
l + x = 40
l = 40 - x ------(1)
Area of the rectangular pen = Length × width
= lx
By substituting the value of l from equation (1),
Area (A) of the pen will be modeled by the expression,
A = (40 - x)
A = 40x - x²
B). For maximum area of the pen,
Derivative of the area = 0
[tex]\frac{d}{dx}(A)=0[/tex]
[tex]\frac{d}{dx}(A)=\frac{d}{dx}(40x-x^2)[/tex]
= 40 - 2x
And (40 - 2x) = 0
x = 20
Therefore, width of the pen = 20 feet
And length of the pen = 40 - 20
= 20 feet
Dimensions of the pen should be 20 feet by 20 feet.
cho f(x)= sign x và g(x) = x(1-x^2). tìm f(g(x))
Answers
Answer:
[tex]f(g(x))= sign(x(1-x^{2})) = sign(x-x^{3})[/tex]
Step-by-step explanation:
How do you do this I’ve been stuck on this
Answers
9514 1404 393
Answer:
x^(1/6)
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)/(a^c) = a^(b-c)
__
Here, we have a=X, b=1/2, c=1/3, so the quotient is ...
(X^(1/2))/(X^(1/3)) = X^(1/2 -1/3) = X^(1/6)
_____
Expressed as a radical, this is ...
[tex]\displaystyle X^{\frac{1}{6}}=\sqrt[6]{X}[/tex]
Answer:
Step-by-step explanation:
x^1/2÷x^1/3=(x)^1/2-1/3= x^1/6--->⁶√x...it's positive answer.
When a fridge is imported, a customs value of 10% must be paid for its value. If the value of the fridge after paying the customs value is rs. 55,000/-. What is the value before paying customs duty?
Answers
Answer:
55000×100/90
61,111.111
Find the missing length indicated
Answers
Answer:
x = 175
Step-by-step explanation:
What is the degree of the monomial 4x7y3
Answers
Answer:
degree 10
Step-by-step explanation:
The degree of the monomial is the sum of the exponents of the variables, so
4[tex]x^{7}[/tex]y³ ← is of degree 10 ( 7 + 3)
Help please!! Based on Pythagorean identities, which equation is true ??
Answers
Answer:
Last answer: [tex]cot^{2} \alpha - csc^{2} \alpha = -1[/tex]
sorry couldn't find theata so I just used alpha.
what 30 + 30+60+(56)-82=?
Answers
94 is the correct answer for that question
Step-by-step explanation:
30+30+60+56-82=94
