Find each trig ratio.

Answer:

A) y=9x

B) y=45 when x=5

Step-by-step explanation:

Part A

\(y=kx\\-27=k(-3)\\-27=-3k\\9=k\\y=9x\)

Part B

\(y=9(5)\\y=45\)

The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer:

14 divided by 4139 is 0.0033824595312878

Step-by-step explanation:

Making a graph of linear inequalities is similar to making a graph of linear equations. But with inequalities, we find a region instead of a line.

What is linear inequality?

Linear inequalities are mathematical statements that are made up of two expressions which are compared using inequality symbols.

The following steps are to be followed to make a graph of linear inequality:-

1. Solve the inequality for y.

2. Considering the inequality as a linear equation graph the line. ( If the inequality sign does not contain an equal sign then draw a dashed line; if the inequality contains an equal sign then draw a solid line.

3. Shade the region that satisfies the inequality.

Hence, a system of linear inequality is graphed similarly to that of a linear equation, but a region is obtained.

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Answer: $8 for 1 hamburger

Step-by-step explanation:

Answer:

Step-by-step explanation:

What you do is multiply the previous number and add 1 to get the next answer.

Equation An = 2(An-1)+1

n = The Term

Answer:

  73/55

Step-by-step explanation:

The cosecant (csc) is one of the reciprocal functions:

  csc(θ) = 1/sin(θ)

  sec(θ) = 1/cos(θ)

  cot(θ) = 1/tan(θ)

So, if we can find the sine, we can find the cosecant.

__

The mnemonic SOH CAH TOA reminds you that the sine is ...

  Sin = Opposite/Hypotenuse

The above tells you that ...

  Csc = 1/Sin = Hypotenuse/Opposite

The hypotenuse of your triangle is AC = 73. The side opposite angle θ is BC = 55. So, the ratio you want is ...

  csc(θ) = 73/55

Answer:

\(csc (\theta)=\frac{33}{55}\)

Step-by-step explanation:

Hello!

1) The cosecant function is the inverse the sine function. So we can write:

\(csc(\theta)=\frac{1}{sin(\theta)}\)

2) The sine function is the side opposite angle to \(\angle \theta\) over the hypotenuse:

\(sin(\theta)=\frac{55}{33}\)

3) So, remembering operations with fractions then the cosecant is:

\(csc \theta = \frac{1}{\frac{55}{33} } =1 \times \frac{33}{55}\)

\(csc (\theta)=\frac{33}{55}\)

Answer:

200 lbs.

Step-by-step explanation:

Divide mass value by 16 to convert oz to lbs.

3,200/16=200

The joint relative Frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.

The joint relative frequency of students who do not like to run and enjoy swimming, we need to find the intersection of the row and column corresponding to those categories in the two-way frequency table.

Given the following information from the table:

Likes running: 28

Does not like running: 46

Column totals: 74

Enjoys swimming: 62

Enjoys cycling: 90

Row totals: 110

The joint relative frequency, we divide the number of students who do not like running and enjoy swimming by the total number of students:

Joint relative frequency = (Number of students who do not like running and enjoy swimming) / (Total number of students)

From the table, the number of students who do not like running and enjoy swimming is given as 46.

Total number of students is given as 74.

Joint relative frequency = 46 / 74

Calculating this value, we find that the joint relative frequency is approximately 0.6216, which is equivalent to 62.16%.

Therefore, the joint relative frequency of students who do not like to run and enjoy swimming is approximately 62.16%.

In conclusion, the joint relative frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.

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Answer:

Step-by-step explanation:

Reciprocal trig functions are opposite or mirror of the normal trig functions. The normal trig functions are as follows:

Sine = opposite side/hypotenuse

Cosine = adjacent side/hypotenuse

Tangent = opposite side/adjacent side

The reciprocals of the above trig ratios would be

Cosecant = hypotenuse/opposite side

Secant = hypotenuse/adjacent side

Cotangent = adjacent side/opposite side

Therefore, looking at the given options, the trigonometric function that can be described as a reciprocal trig function is

D. sec(0)

The answer to the expression is  (x+3)/(x-1)

You should recall that a quadratic expression is an algebraic expression of the form ax2 + bx + c = 0, where a ≠ 0

The given expressions are

(x² - 3x - 18) / (x²- 7x +6

(x²-6x +3x +19) / (x²-x -6x +6)

This implies that {(x²-6x)+(3x-18)} / {(x²-x) -(6x+6)}

⇒[x(x-6)+3(x-6)] / [x(x-1) - 6(x-1)]

This means that [(x+3)(x-6)] / [(x-6)(x-1)]

Dividing by (x-6) to have

Therefore the value of the expression is (x+3)/(x-1)

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Answer:

The data given is  

    235,000 271,900 183,300 203,000 182,900 225,500 189,000 214,200 237,900 233,500 217,000 230,400 202,950, 216,500 209,900, 245,500

  The sample size is  n =  16

   The population is  \(\mu  =  \$201,800\)

  The sample mean is mathematically represented as

             \(\= x =\frac{\sum x_i}{n}\)

=>  \(\= x  =\frac{235,000 + 271,900 + \cdots + 245,500 }{16}\)

=>    \(\= x  = 218653.125\)

Generally the sample standard deviation is mathematically represented as

     \(s =  \sqrt{\frac{\sum (x_i - \= x)^2}{n} }\)

=>   \(s =  \sqrt{\frac{ (235,000 -  218653.125)^2+ (271,900 -  218653.125)^2 + \cdots +  (245,500 -  218653.125)^2}{16} }\)

=>   \(s =  23946.896 \)

The null hypothesis is  \(H_o : \mu =  \$201,800\)

The alternatively hypothesis is  \(H_o : \mu >  \$201,800 \)

Generally the test statistics is mathematically represented as

     \(t =  \frac{\= x  - \mu }{ \frac{s}{\sqrt{n} } }\)

=>  \(t =  \frac{218653.125  - 201800 }{ \frac{23946.896 }{\sqrt{16} } }\)

=>  \(t =  2.82\)

Generally the degree of freedom is mathematically represented as

     \(df =  n - 1\)

=>   \(df =  16 - 1\)

=>   \(df =  15\)

Generally the probability of  \(t =  2.82\) at a degree of freedom of  \(df =  15\) from the t - distribution table  is  

     \(p-value  = P( t >2.82 ) =0.00646356\)

The

From the values obtained we see that \(p-value  < \alpha\)

The decision rule is  

   Reject the null hypothesis

The conclusion is

 There is sufficient evidence to conclude that the real estate company's  projection is true

Given that the population variance is unknown then the best statistical distribution to be applied is the t -distribution

Type I  Error

 The type 1 error occur when the null hypothesis is wrongfully rejected

  The consequence in this case is the company will assume that the average selling price has increase and this will lead the company to start expanding the business while in the real sense the average selling price is still  $201,800

   Type II  Error

 The  type 11 error occur when the null hypothesis is wrongfully  accepted(i.e wrongfully failed to reject the null hypothesis)

    The consequence in this case is that the company will assume that the average selling price  is still $201,800 and will not make plans to increase the business while in the real sense the average selling price has increased

   Given that resource is scare the management of the company will want a  smaller  significance level in order not to commit type I error which will lead to wrongly expanding the business and wastes of resources

generally the critical value  of  \(\frac{\alpha }{2}\) from the normal distribution table is    

     \(Z_{\frac{\alpha }{2} } = 1.96\)

Generally the margin of error is mathematically represented as

   \(E  =Z_{\frac{\alpha }{2} } *  \frac{s}{\sqrt{n} }\)

=>\(E  =1.96*  \frac{23946.896}{\sqrt{16} }\)

=>\(E  = 11733.96\)

Generally the 95% confidence interval is  mathematically represented as

     \(218653.125 - 11733.96  < \mu  <  218653.125 + 11733.96\)

=>  \(206919.165  < \mu  <  230387.085\)  

Generally there is 95% confidence that the actual average selling price is within this interval  

Step-by-step explanation:

The simplification of  (39x⁵z⁴)⁰ • 18x²y  is 18x²y.

Making anything simpler is known as simplification. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.

To simplify an equation:

Rewrite the given equation using the commutative property of multiplication.

18(39x⁵z⁴)⁰x²y

Use the power rule (xy)ⁿ=xⁿyⁿ for distributing the exponent.

18(39⁰(x⁵)⁰(z⁴)⁰)x²y

Anything raised to 0 is 1.

18(1(x⁵)⁰(z⁴)⁰x²y

Multiply (x⁵)⁰(x⁵)⁰ by 11.

18((x⁵)⁰(z⁴)⁰)x²y

Multiply the exponents in (x⁵)⁰.

18(x⁰(z⁴)⁰)x²y

Multiply x⁰ by x² by adding the exponents.

18(x²(z⁴)⁰)y

Simplify 18(x²(z⁴)⁰)y

18x²y

Therefore, simplification of given equation is 18x²y.

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The equation of the line passing through the points (-2,1) and (2,-11) the previous is -3 is -3x - 4.

It is also commonly represented by the variable "m" in the equation of a line: y = mx + b. A positive slope indicates that the line rises as x increases, a negative slope indicates that the line falls as x increases, and a slope of zero indicates that the line is horizontal.

The equation of the line with slope -3 and passing through the point (-2,1) can be found using point-slope form of a line:

y - 1 = -3 (x + 2)

y = -3x - 5 + 1

y = -3x - 4

The equation of the line passing through the points (-2,1) and (2,-11) is y = -3x - 4.

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Answer:

A is correct

Step-by-step explanation:

Answer:

it's A -2/9

Step-by-step explanation:

it's A

it's A

Answer:

I think 60

Step-by-step explanation:

have a great day

Answer:

The answer is $300

Step-by-step explanation:

15 dollars per lawn times 5 lawns per day is $75 and 75×4 is 300

Answer

Explanation

Given

• Fay can prepare surgical equipment in 3 hours.

• Carol, can do it in 4 hours.

• How long will it take if they work together?​

Procedure

If Fay can do the entire work in 3h, and Carol in 4h, then:

• Fay can do 1/3 of the job per hour,

• Carol can do 1/4 of the job per hour,

Thus, assuming that their labors are additive and they never get in each other's way, we can add together what they can do individually per hour:

Then, they can do 7/12 per hour

Answer:

49

Step-by-step explanation:

First multiply 3 x 5.Which will give you 15.Then add 34 and 15 which will give you 49.

Answer:

49

Step-by-step explanation:

3 x 5 = 15

15+34 = 49

Answer:

Mrs. Hinds can expect 480 students to choose hamburger for lunch.

Step-by-step explanation:

Mrs. Hinds originally asks 30 students.
If she asks all 1200 students in the school, she would have to divide 1200 by 30.
1200 ÷ 30 = 40
Now she has to multiply 40 by how many students originally wanted hamburger.
40 × 12 = 480
Mrs. Hinds can expect 480 students to choose hamburger for lunch.

We have the following:

Now, if we deduct the taxes we have:

The answer is $205.92

Answer:

8 years

Step-by-step explanation:

Shaniquas age is given as 36. This age is going to help us to find the rest.

Pablo is said to 1/3 of Shaniquas age

= 1/3 of 36 = 36/3 = 12

Pablo is 12

Danny is younger than pablo by 1

12 - 1 = 11

Danny is 11

Terrell is younger than danny by 3

11-3 = 8

Terrell is 8 years old

Answer:

I think ur profile pic is cute

Step-by-step explanation:

Step-by-step explanation:

1 is the starting point since it is on the the axis.

then you would use the rise over run method to get the fraction. it rises by two and runs by 1 which would get you 2/1. so the answer should be y=1+2/1

(it is an addition sign since it is a positive slope)

Answer:

0.25x -12= 18- 0.55x (subtract 0.25x from both sides)

-12= 18 -0.80x (subtract 18 from both sides)

-30= -0.80x (divide each side by -0.80)

x= 37.5 (this is your answer)

The value of x in which the two expressions have the same value is 37.5

Here,

Given that;

Two expressions are,

Expression 1 :   0.25x - 12

Expression 2:   18- 0.55x

We have to find the value of x.

What is Mathematical expression?

A sentence with a minimum of two numbers or variables and at least one math operation is present, is called Mathematical expression.

Now,

The value of x will be find after equating both expressions as;

0.25x - 12 = 18 - 0.55x

Subtract 0.25x from both sides, we get;

- 12 = 18 - 0.80x

Subtract 18 from both side, we get;

- 30 = - 0.80x

Divide each side by -0.80, we get;

x= 37.5

Hence, The value of x in which the two expressions have the same value is 37.5

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Answer:

\(\mathbf{((lnx)(2x^2)) -x^2 +39 =(2y^2 +(\dfrac{4}{3})(8+y^2)^{3/2})}\)

Step-by-step explanation:

Given that:

\(x In(x) = y( 1+ \sqrt{8+ y^2}) \ } \ \dfrac{dy}{dx}\)

\(xln(x) *dx= (y+y \sqrt{(8+y^2}) \ dy\)

\(\int xln(x) dx = \int(y+y\sqrt{(8+y^2})) \ dy\)

\(\int lnx (x)dx =(\dfrac{y^2}{2} +\dfrac{1}{3}(8+y^2^{)3/2})\)

\((lnx \dfrac{x^2}{2})-\int((\dfrac{x^2}{2})\times \dfrac{1}{x} =(\dfrac{y^2}{2} +\dfrac{1}{3}(8+y^2)^{3/2})\)

\(((lnx)(\dfrac{x^2}{2}))-\int(\dfrac{x}{2}) =(\dfrac{y^2}{2} +(\dfrac{1}{3})(8+y^2)^{3/2})\)

\(((lnx)(\dfrac{x^2}{2}))-(\dfrac{x^2}{4}) +C= (\dfrac{y^2}{2 }+(\dfrac{1}{3})(8+y^2)^{3/2})\)

For  y(1) = 1

\(((ln(1))(\dfrac{1^2}{2}))-(\dfrac{1^2}{4}) +C= (\dfrac{1^2}{2 }+(\dfrac{1}{3})(8+1^2)^{3/2})\)

\((0)-(\dfrac{1}{4}) +C =(\dfrac{1}{2} +(\dfrac{1}{3})(3)^3)\)

\(C=(\dfrac{19}{2}) +(\dfrac{1}{4})\)

\(C=\dfrac{39}{4}\)

\(((lnx)(\dfrac{x^2}{2}))-(\dfrac{x^2}{4}) +(\dfrac{39}{4}) = (\dfrac{y^2}{2} +(\dfrac{1}{3})(8+y^2)^{3/2})\)

\(\mathbf{((lnx)(2x^2)) -x^2 +39 =(2y^2 +(\dfrac{4}{3})(8+y^2)^{3/2})}\)

9514 1404 393

Answer:

  3 feet per second

Step-by-step explanation:

If the time is multiplied by 2, the inverse relationship tells you the speed is multiplied by 1/2.

  (1/2)(6 ft/s) = 3 ft/s

The swimmer's average speed is 3 ft/s.

Answer:

Answer is option  D

Step-by-step explanation:

Hope this helps:)

Answer:

52 : 39 56 : 42 60 : 45

64 : 48 68 : 51

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(log\ \frac{1}{x} = - log \ x \\\\log_a \ a = 1\\\\log \ a^x = x \ log \ a\)

(iii)

\(m = log_2 \ \frac{1}{32}\\\\m = log_2 \ \ 32^{-1}\\\\m = - 1 \ log_2 32\\\\m = - 1 \ log_2 \ 2^5\\\\m = -1 \times 5 \ log_2 \ 2\\\\m = -5 \ log_2 \ 2\\\\m = -5 \times 1 = -5\)

(iv)

\(log_a \ m = 0\\\\m = a^0 = 1\)                       \([ \ log _a \ 1 = 0 \ ]\)

(vii)

\(log_{32} \ 8 = m\\\\8 = 32^m\\\\8^{ \frac{1}{m}} = 32 \\\\(2^{3 })^ { \frac{1}{m}} = 2^{5}\\\\2^{\frac{3}{m}} = 2^5 \\\\\frac{3}{m} = 5\\\\3 = 5 \times m \\\\m = \frac{3}{5}\)

(viii)

\(log_5 \ ( 2m + 5 ) = 3\\\\(2m +5 ) = 5^3\\\\2m + 5 = 125\\\\2m = 125 - 5 \\\\2m = 120 \\\\m = 60\)

(x)

\(log_{m^3} \ 64 = \frac{2}{3}\\\\64 = (m^3)^{ \frac{2}{3}}\\\\64 = m^{ 3 \times \frac{2}{3}}\\\\64 = m ^2\\\\\sqrt{64} = m \\\\8 = m\)

Answer:

  (x, y) = (0.5, 4) or (4, 0.5)

Step-by-step explanation:

The given equations are more easily solved by making the bases of the logarithms all the same. Then we can use substitution to form a quadratic equation that will give two solutions to the problem.

Rewriting the first equation to use base-2 logarithms, we have ...

  \(\log_4(xy)=\dfrac{1}{2}\qquad\text{given}\\\\\dfrac{\log_2(xy)}{\log_2(4)}=\dfrac{1}{2}\qquad\text{change of base formula}\\\\\dfrac{\log_2(x)+\log_2(y)}{2}=\dfrac{1}{2}\qquad\text{evaluate $\log_2(4)$, separate variables}\\\\\log_2(y)=1-\log_2(x)\qquad\text{solve for $\log_2(y)$}\)

Substituting this expression into the second equation gives a quadratic in log₂(x).

  \(\log_2(x)(1-\log_2(x))=-2\qquad\text{substitute for $\log_2(y)$}\\\\\log_2(x)^2-\log_2(x)-2=0\qquad\text{put quadratic in standard form}\\\\(\log_2(x)-2)(\log_2(x)+1)=0\qquad\text{factor the quadratic}\)

Solutions are values of log₂(x) that make the factors zero:

  log₂(x) -2 = 0   ⇒   log₂(x) = 2   ⇒   x = 2² = 4

  log₂(x) +1 = 0   ⇒   log₂(x) = -1   ⇒   x = 2⁻¹ = 1/2

The corresponding values of y are the other value of x:

  log₂(y) = 1 -log₂(x) = 1 -2 = -1   ⇒   y = 1/2  for  x = 4

  log₂(y) = 1 -log₂(x) = 1 -(-1) = 2   ⇒   y = 4  for  x = 1/2

Solutions are ...

  (x, y) = (4, 1/2)  or  (1/2, 4)

__

Additional comment

The attachment shows a graphing calculator solution to the original pair of equations.

Answer:

m ≤ 5

Step-by-step explanation:

I will begin by assuming m to be the number.

Then, the sum of m and 3 is: m + 3.

The symbol for "less than or equal to" is ≤.

So we form an inequality, like this :

m + 3 ≤ 8

To find m subtract 3 on each side:

m ≤ 5

Therefore, m ≤ 5.