Answer:
Following are the ratio to this question:
Step-by-step explanation:
Given:
[tex]\bold{\tan \phi = \frac{60}{11} }\\\\[/tex]
Formula:
[tex]\sin \phi = \frac{Perpendicular}{Hypotenuse}\\\\\cos \phi = \frac{Base}{Hypotenuse} \\\\\tan \phi = \frac{Perpendicular}{Base} \\\\\ cosec \phi = \frac{Hypotenuse}{Perpendicular}\\\\\sec \phi =\frac{Hypotenuse}{Base}\\\\\cot \phi = \frac{Base}{Perpendicular}\\\\[/tex]
[tex]\ Base = 11 \\\ Perpendicular =60\\\ Hypotenuse= 61\\[/tex]
[tex]\sin \phi = \frac{60}{61}\\\\\cos \phi = \frac{11}{61} \\\\\tan \phi = \frac{60}{11} \\\\\ cosec \phi = \frac{ 61}{60}\\\\\sec \phi =\frac{61}{11}\\\\\cot \phi = \frac{11}{60}\\\\[/tex]
What is the range of a function?
Answer:
The set of all output values of a function. Example: when the function f(x) = x2 is given the values x = {1,2,3,...} then the range is {1,4,9,...}
What can you conclude about the hypotenuse of the two triangles?
Answer: C
Step-by-step explanation:
Since the sides are marked with the little lines, you know they are congruent with each other. Since the sides are congruent, you know the hypotenuse will be congruent.
You can argue that these triangles are similar, but the difference is that similar triangles are the same shape, but not the same size. These triangles are congruent because they are the same size and shape. Therefore, the hypotenuse is congruent.
A 14 gram sample of a substance that's used to preserve fruit and vegetables has a k-value of 0.1092. Find the substance's half-life, in days. Round your answer to the nearest tenth. N=Noe^-kt
Answer:
t = 6.3
Step-by-step explanation:
N=Noe^(-kt)
No = 14 grams
k = .1092
We want to find t when N = 7 or 1/2 of 14
N=Noe^(-kt)
7 = 14 e ^ (-.1092t)
Divide each side by 14
1/2 = e ^ (-.1092t)
take the natural log of each side
ln (1/2) = ln e ^ (-.1092t)
ln (1/2) = -.1092t
Divide each side by -.1092
ln (1/2)/ -.1092 = t
t≈6.3475
Rounding to the nearest tenth
t = 6.3
Answer: 6.3
Step-by-step explanation:
The average amount of rain per year in Greenville is 49 inches. The standard deviation is 8 inches. Find the probability that next year Greenville will receive the following amount of rainfall. Assume the variable is normally distributed.
A) At most 55 inches of rainB) at least 62 inches of rainC) Between 46 and 55 inches of rainD) How many inches of rain would you consider to be an extremely wet year?
Answer:
The probability that next year Greenville will receive the following amount of rainfall A) At most 55 inches of rain is 0.7734, B) at least 62 inches of rain is 0.0516, C) Between 46 and 55 inches of rain is 0.0387
D Having rainfall of above 65 inches would be considered as an extremely wet year
Step-by-step explanation:
A. To find the probability that next year Greenville will receive at most 55 inches of rain we would have to make the following calculation:
P(X<55)
=P((X-mean)/s<(55-49)/8)
=P(Z<0.75)
=0.7734
The probability that next year Greenville will receive at most 55 inches of rain is 0.7734
B. To find the probability that next year Greenville will receive at most 62 inches of rain we would have to make the following calculation:
P(X>62)
=P(Z>(62-49)/8)
=P(Z>1.63)
=0.0516
The probability that next year Greenville will receive at most 62 inches of rain is 0.0516
C. To find the probability that next year Greenville will receive at Between 46 and 55 inches of rain we would have to make the following calculation:
P(46<X<54)
=P((46-49)/8 <Z<(54-49)/8)
=P(-0.38 <Z< 0.63)
=0.3837
The probability that next year Greenville will receive Between 46 and 55 inches of rain is 0.3837
D. Here consider a value that is more two standard deviations above the mean as an unusual vale. That is:
X=2σ+μ
=2(8)+49
=65
Therefore, having rainfall of above 65 inches would be considered as an extremely wet year.
What is the square root of -1
Answer:
i
Step-by-step explanation:
It's imaginary, or it can also be referred to as i.
Solve (x + 1)2 - 4(x + 1) + 2 = 0 using substitution.
U=
х
4(x +1)
O x +1
(x + 1)2
Answer:
Step-by-step explanation:
We are given the equation [tex](x+1)^2-4(x+1)+2=0[/tex]. Consider the substitution u = (x+1). Then the equation turns out to be [tex]u^2-4u+2=0[/tex]
Recall that given a second degree polynomial of the form [tex]ax^2+bx+c =0[/tex] then its solutions are given by the expression
[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]
In our case, a = 1, b = -4 and c =2. Then the solutions are
[tex]u_1 = \frac{4+\sqrt[]{(-4)^2-4(2)}}{2} = 2 +\sqrt[]{2}[/tex]
[tex]u_2 = \frac{4-\sqrt[]{(-4)^2-4(2)}}{2} = 2 -\sqrt[]{2}[/tex]
We have that x = u-1. So the original solutions are
[tex]x_1 = 2 +\sqrt[]{2}-1 = 1 + \sqrt[]{2}[/tex]
[tex]x_2 =2 -\sqrt[]{2} -1 = 1 - \sqrt[]{2}[/tex]
Answer: x+4
Step-by-step explanation: part one- x+4
Part two- 3+sqrt21 over 2 +4 & 3- sqrt21 over 2 +4
A community center sells a total of 305 tickets for a basketball game. An adult ticket costs $5. A student ticket costs $1. The sponsors collect $693 in ticket sales. Find the number of each type of ticket sold.
Answer: student tickets = 208
Adult tickets = 97
Step-by-step explanation:
x + y = 305
x = 305 - y
5x + y = 693
Substituting
5 (305 - y) + y = 693
1525 - 5y + y = 693
-4y = -832
y = 832 / 4 = 208
45% of 40 is 18% of what number?
Answer:
100
Step-by-step explanation:
40 / 100= .4
.4 x 45 = 18
18/18= 1
1x 100= 100
Answer:
100
Step-by-step explanation:
:D
(3xy)*x*у
х
Зуз
Зхуз
9xуз
9x5уз
Answer:
3 x^2 y^2
Step-by-step explanation:
Simplify the following:
3 x y x y
3 x y x y = 3 x^2 y^2:
Answer: 3 x^2 y^2
PLEASEE HELP ME!!!!!!
Answer:
I). X= 1,0. II) 1.72
Step-by-step explanation:
Using quadratic formula
To the nearest degree, what is the measure of the central angle for faucets?
Answer:
43°
Step-by-step explanation:
The city of Eden completed a new light rail system to bring commuters and shoppers into the downtown area and relieve highway congestion. City planners estimate that each year, 15% of those who drive or ride in an automobile will change to the light rail system; 80% will continue to use automobiles; and the rest will no longer go to the downtown area. Of those who use light rail; 5% will go back to using an automobile, 80% will continue to use light rail, and the rest will stay out of the downtown area. Assume those who do not go downtown will continue to stay out of the downtown area. The transition matrix associated with this Markov chain is a.an absorbing stochastic matrix. b.a regular stochastic matrix.
Answer:
Step-by-step explanation:
To check which option is correct we will first make transition matrix.
Let the state 1 and state 2 represent the automobile and light rail
So, the transition is given by
[tex]P=\left[\begin{array}{ccc}0.80+0.05&0.15\\0.5+0.15&0.80\end{array}\right][/tex]
[tex]P=\left[\begin{array}{ccc}0.85&0.15\\0.20&0.80\end{array}\right][/tex]
Since P as no any entry zero so, P as not absorbing stochastic matrix
Also,
[tex]|P| = \left|\begin{array}{ccc}0.85&0.15\\0.20&0.80\end{array}\right| \\\\=0.85\times0.8-0.15\times0.2\\\\=0.65\neq0[/tex]
since |P| ≠ 0
Hence, Markov chain is a regular stochastic matrix.Solve the system using substitution.
5x+ 4y = 10
4x - y = 8
Answer:
Step-by-step explanation:
hello
from 4x-y=8 we can say that y = 4x-8
we substitute in the first equation to get
5x + 4 (4x-8) = 10
then
5x + 16 x -32 = 10
<=> 21x = 32+10=42
<=> x = 42/21 = 2
and then y = 8-8=0
don t hesitate if you need any further explanation
thanks
Answer: x = 2, y = 0 or (2 , 0)
Step-by-step explanation:
Solving using substitution is where you solve for a variable in one of the two equations in the system then plug it into the other.
For an easier plug in we can take the second equation. 4x-y = 8.
From here we need to isolate the y variable which is easier to isolate than x, in my opinion.
Subtract the 4x over.
-y = 8-4x
Now divide by a -1 so y is positive.
y= -8 + 4x
Now plug this in for y in the other equation.
5x + 4(-8 + 4x) = 10
Distribute the 4.
5x - 32 + 16x = 10
Combine like terms
21x - 32 = 10
Add the 32.
21x = 42
Divide by 21.
x = 2
Now that we have solved for one variable we can plug this into either equation and solve for the other.
I will plug it into the second equation.
4(2) - y = 8
Simplify.
8 - y = 8
Subtract 8.
-y = 0
Divide by -1.
y = 0
So the x and y values are.
x = 2
y = 0
The sum of the two digits of a certain two-digit number equals the square root of the number? What is the number?
Answer:
81
Step-by-step explanation:
2-digit squares are 16, 25, 36, 49, 64, 81.
Their sums of digits, are ...
7, 7, 9, 13, 10, 9
The square 81 has a sum of digits equal to its square root.
what is the percentage 33% of $145.00
Answer:
47.85
Step-by-step explanation:
33% of 145
of means multiply
Changing to decimal form
.33* 145
47.85
Step-by-step explanation:
cross multiply, set up ur equation like so
33. x
100 = 145
100x=4785
100
x=47.85
The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.67 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.8 inches and a standard deviation of 2.54 inches. What percentage of men are SHORTER than 67 inches
Answer:
14.69% of men are SHORTER than 67 inches
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.67 inches.
This means that [tex]\mu = 69.8, \sigma = 2.67[/tex]
What percentage of men are SHORTER than 67 inches
This is the pvalue of Z when X = 67. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{67 - 69.8}{2.67}[/tex]
[tex]Z = -1.05[/tex]
[tex]Z = -1.05[/tex] has a pvalue of 0.1469
14.69% of men are SHORTER than 67 inches
In a bag of skittles 12 are yellow, 10 purple, 8 red, 9green and 22 orange. If 5 were selected from the bag. Calculate using counting technique what is the probability that:
A). exactly 2 are red
B). At most 2 are red
Answer:
a) 11.03% probability that exactly two are red.
b) 98.64% probability that at most 2 are red.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the order in which the skittles are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
12 + 10 + 8 + 9 + 22 = 61 skittles.
A). exactly 2 are red
Desired outcomes:
2 red, from a set of 8.
3 non-red, from a set of 61 - 8 = 53.
So
[tex]D = C_{8,2}*C_{53,3} = \frac{8!}{2!(8-2)!}*\frac{53!}{3!(53-3)!} = 655928[/tex]
Total outcomes:
Five skittles from a set of 61. So
[tex]T = C_{61,5} = \frac{61!}{5!(61-5)!} = 5949147[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{655928}{5949147} = 0.1103[/tex]
11.03% probability that exactly two are red.
B). At most 2 are red
Desired outcomes:
None red(5 from a set of 53)...
One red(from a set of 8), and four non-read(4 from a set of 53).
Two red(655928), as found in a.
So
[tex]D = C_{53,5} + C_{8,1}*C_{53,4} + 655928 = \frac{53!}{5!48!} + \frac{8!}{1!7!}*\frac{53!}{4!49!} + 655928 = 5868213[/tex]
Total outcomes:
Five skittles from a set of 61. So
[tex]T = C_{61,5} = \frac{61!}{5!(61-5)!} = 5949147[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{5868213}{5949147} = 0.9864[/tex]
98.64% probability that at most 2 are red.
Apple would like to estimate the web browsing battery life of the iPad. The following data represents the battery life, in hours, experienced by six users.
10 14 14 16 13 8
Using this sample, the point estimate for the web browsing battery life of the iPad is:________
Answer:
12.5 hours
Step-by-step explanation:
The data which represents the battery life, in hours, experienced by six users is given below:
10 14 14 16 13 8
To determine the point estimate for the web browsing battery life of the iPad, we find the mean number of hours.
[tex]Mean=\dfrac{10+14+14+16+13+8}{6} \\\\=\dfrac{75}{6} \\\\=12.5[/tex]
The point estimate for the web browsing battery life of the iPad is: 12.5 hours
Which inequality represents the sentence below? Four and nine tenths less than the product of a number and six is no more than eighteen and one-eighth. 4 and StartFraction 9 over 10 EndFraction minus 6 x less-than-or-equal-to 18 and StartFraction 1 over 8 EndFraction 6 x minus 4 and StartFraction 9 over 10 EndFraction less-than-or-equal-to 18 and StartFraction 1 over 8 EndFraction 4 and StartFraction 9 over 10 EndFraction less-than 6 x + 18 and StartFraction 1 over 8 EndFraction 6 x minus 4 and StartFraction 9 over 10 EndFraction less-than 18 and StartFraction 1 over 8 EndFraction
Answer:
D. 6x-4 9/10<= 18 1/8
Step-by-step explanation:
Sorry I'm a little late :(
Please answer this correctly without making mistakes
Answer:
It would be 131.95 if they want the answer in pi it would be 42 pi
Step-by-step explanation:
3 1/3 + (-2 1/4) + 1 5/6=
Answer:
[tex]2\dfrac{11}{12}[/tex]
Step-by-step explanation:
The first step is to ensure that all of the fractions have a common denominator.
[tex]3\dfrac{1}{3}+\left( -2\dfrac{1}{4} \right) + 1\dfrac{5}{6}= \\\\3\dfrac{4}{12} - 2\dfrac{3}{12} +1 \dfrac{10}{12}= \\\\1\dfrac{1}{12}+1\dfrac{10}{12}= \\\\\boxed{2\dfrac{11}{12}}[/tex]
Hope this helps!
How many solutions does the equation –2(3x – 1) = –6x – 1 have?
What about 2(3x – 1) = 6x – 2?
What about 2(3x – 1) = –6x – 2?
Answer: See below
Step-by-step explanation:
–2(3x – 1) = –6x – 1
-6x + 2 = -6x - 1 (IMPOSSIBLE, ZERO)
2(3x – 1) = 6x – 2
6x - 2 = 6x - 2 (INFINITE)
2(3x – 1) = –6x – 2
6x - 2 = -6x - 2 (ONE, x can be the number 0)
How much of other chemicals must be evaporated from 400 grams of a hand sanitizer
that is 24% alcohol to strengthen it to a hand sanitizer that is 30% alcohol? Correct your
answer to the nearest whole number.
Answer:
24 g
Step-by-step explanation:
We first find the mass of 24 % alcohol in 400 g of hand sanitizer. Let x be the mass of alcohol. So, x/400 × 100 % = 24 %
x/400 = 0.24
x = 0.24 × 400
= 96 g
The mass of the other chemicals is thus 400 g - 96 g = 304 g
We now find the mass of 30 % alcohol in 400 g of hand sanitizer. Let y be the mass of alcohol. So, y/400 × 100 % = 30 %
y/400 = 0.30
y = 0.30 × 400
= 120 g
The mass of the other chemicals is thus 400 g - 120 g = 280 g
The mass of other chemicals that needs to be evaporated is thus 304 g - 280 g = 24 g
H is directly proportional to the square root of p h= 5.4 when p = 1.44 find h when p =2.89
Answer:
h=7.65
Step-by-step explanation:
H is directly proportional to the square root of p;
Let k be the constant of proportionality;
Means h=k√p
This means for corresponding points of h and p such that (h1,p1) and (h2,p2) we have;
h1/√p1=h2/√p2
Let h= 5.4 when p = 1.44 and h when p =2.89 be respectively (h1,p1) and (h2,p2)
So that
5.4/√1.44=h/√2.89
5.4/√1.44 ×√2.89 = h
7.65= h
h=7.65
A researcher was interested about the weekly average usage of a local park in San Antonia, Texas. A study was designed to study the relationship between age and number of times residents visited the park each week. They were interested to see if age tends to impact the number of times residents visit the park. The surveyor collected responses information about age and the number of visits per week from 118 residents of San Antonia, Texas. They provided them with an anonymous paper survey to fill out.
Required:
a. What are the observational units in this study?
b. Is number of visits per week the explanatory or response variable?
c. Is age the explanatory or response variable?
d. Is this an observational study or a randomized experiment?
e. What is the most concerning type of bias in this study? Why?
f. What is the appropriate scope of inference in this study
Answer:
a) Residents of San Antonia, Texas
b) Response variable
c) Explanatory variable
d) Observational study
e) Response bias
f) The appropriate scope of interest is the " relationship between age and the weekly average usage of local parks in San Antonia"
Step-by-step explanation:
a) In this study, the objects or entities on which observation is done are the residents of San Antonia, hence they are the observational units.
b) In this observation, the number of visits per week is the response variable because it is the outcome of the observation. It is a dependent variable that varies due to variation in the ages.
c) Age is the variable that helps to predict the average number of visits to the park, it can then be called the predictor variable. It is independent of any external variable.
d) This is an observational study because it is meant to observe the relationship between the ages and the average number of visits to the park per week. The variables are not randomly assigned.
e ) The type of bias that is most concerning in this study is response bias. This is because it is a paper survey and their can be invalid responses either due to unfaithfulness or ignorance of the respondents.
f) The appropriate scope of the inference in this study is the relationship between the ages and the weekly average usage of local parks in San Antonia.
Find the area of the trapezoid with the numbers 4, 3, 3 ,1
Answer:
The answer depends on the shape of the trapezoid...
Step-by-step explanation:
A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel. (trapezium)
Area = (a+b/2) * h
IF the sides are a = 3 ,b = 3 and height = 4
THEREFORE:
(3+3/2) * 4
6/2 * 4
3 * 4
12
Hope it helped.... Please mark as brainliest..thanks!!!
Which graph represents the following system of inequalities? Y>5x-1 and then y less than or equal to x+3 please it's for Plato
Answer:
y=3
Step-by-step explanation:
If we use LCM and take 3 plus y it equals x so if x equals x it is then y
Answer:
D
Step-by-step explanation:
I took the Plato Course
What is a factor of 10 but not a multiple of 2
5
Step-by-step explanation:
5 goes into 10 but 2 does not go into 5
Line segment Q R , Line segment R S are Line segment S Q midsegments of ΔWXY. Triangle R Q S is inside triangle X Y W. Point R is the midpoint of side X Y, point S is the midpoint of side Y W, and point Q is the midpoint of side X W. The length of Q R is 2.93 centimeters, the length of R S is 2.04 centimeters, and the length of Q S is 2.28 centimeters. What is the perimeter of ΔWXY? 11.57 cm 12.22 cm 12.46 cm 14.50 cm
Answer:
14.50 cm
Step-by-step explanation:
The Midsegment Theorem states that the midsegment connecting the two sides of a triangle is parallel to the third side, and its length is half that of the third side.
Thus, ∆XYZ is similar to ∆QRS with a scale factor of 2.
Also, the perimeter of ∆XYZ is twice that of ∆QRS.
For ∆QRS, P = 2.93 cm + 2.04 cm + 2.28 cm = 7.25 cm
∴ The perimeter of ∆XYZ = 2 × 7.25 cm =14.50 cm
The Perimeter of triangle WXY is 14.5cm
The formula for calculating the perimeter of the triangle WXY is given as:
Perimeter of triangle WXY = XY + YZ + XY
From the given triangle;
QR = 2.93cmQS = 2.28cmRS = 2.04cmAlso,
XR = RY = QR = 2.93cmZS = SY = QS = 2.28cmZQ = QX = RS = 2.04cmPerimeter of triangle WXY = 2QR + 2QS + 2RS
Perimeter of triangle WXY = 2(2.93) + 2(2.28) + 2(2.04)
Perimeter of triangle WXY = 5.86 + 4.56 + 4.08
Perimeter of triangle WXY = 14.5cm
Hence the Perimeter of triangle WXY is 14.5cm
Learn more on perimeter of triangles here: https://brainly.com/question/24382052
Solve the following equation using the quadratic formula: 3(x+4)2 - 81 = 0
Answer:
[tex]-4\pm 3\sqrt{3}[/tex]
Step-by-step explanation:
[tex]3(x+4)^2-81=0 \\\\3(x^2+8x+16)-81=0 \\\\3x^2+24x+48-81=0 \\\\3x^2+24x-33=0 \\\\x=\dfrac{-24\pm\sqrt{24^2+4(3)(33)}}{2(3)}= \\\\\dfrac{-24\pm\sqrt{972}}{6}= \\\\\dfrac{-24\pm 18\sqrt{3}}{6}= \\\\-4\pm 3\sqrt{3}[/tex]
Hope this helps!
