Use the number line​ below, where RS=4y+4​, ST=3y+8​, and RT=54.
a. What is the value of​ y?
b. Find RS and ST.

The equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S

To answer the question, we need to know what an equation is

An equation is a mathematical expression that show the relationship between two variables.

Given 9cos(sin¯¹(x)) = √(81 – 81x²), we need to show L.H.S = R.H.S

So, L.H.S = 9cos(sin¯¹(x))

= 9[√{1 - sin²(sin¯¹(x)}] (Since sin²y + cos²y = 1 ⇒ cosy = √[1 - sin²y])

9[√{1 - sin²(sin¯¹(x)}] = √9² × √{1 - sin²(sin¯¹(x)}]

= √[9² × {1 - sin²(sin¯¹(x)}]

= √[81 × {1 - sin²(sin¯¹(x)}]

= √[81 × {1 - x²}]   (since sin²(sin¯¹(x) = [sin(sin¯¹(x)]² = x²)

= √(81 – 81x²)

= R.H.S

So, the equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S

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Answer:

a=0

Step-by-step explanation:

If this is what you are asking, and if I understand it correctly, 8*8=64 and not 8, but 8*0=0, therefore 0 is a solution.

Answer:

D

Step-by-step explanation:

substitute x = 4 , y = - 5 into the expression

[tex]\frac{8(4)(-5)+16(-5)}{5(4)}[/tex]

= [tex]\frac{-160-80}{20}[/tex]

= [tex]\frac{-240}{20}[/tex]

= - 12

Answer:

$31,341.81

Step-by-step explanation:

The compound amount equation is A = P(1 + r/n)^(nt), where P is the unknown principal, r is the annual interest rate, n is the number of compounding periods per year and t is the number of years.  We want to solve this for P:

       A

------------------- = P

(1 + r/n)^(nt)

Substituting the given numerical values;

     $45,000

 ---------------------------  =  P

   (1+0.073/4)^(4*5)

Using a calculator, we evaluate this expression, obtaining:  $31,341.81

Using the t-distribution, the 95% confidence interval within which the mean of the total population of such cases is expected lie is:

(112.5, 127.5).

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 18 - 1 = 17 df, is t = 2.1098.

The parameters for this problem are:

[tex]\overline{x} = 120, s = 15, n = 18[/tex].

Hence the bounds of the interval are:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 120 - 2.1098\frac{15}{\sqrt{18}} = 112.5[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 120 + 2.1098\frac{15}{\sqrt{18}} = 127.5[/tex]

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SOLUTION :

let total people in the party be x i.e. 1260

then , number of men = 5/9 of x

= 5/9 of 1260 = 5 × 140 = 700 men

now ,

number of women = Total person - (number of total men)

= ( 1260 - 700 ) women

= 560 women

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The measure of the indicated angle to the nearest degrees is 23 degrees.

The angle of a right angle triangle can be found as follows:

Therefore, the angle can be found using trigonometric ratios as follows;

cos ∅ = adjacent / hypotenuse

Therefore,

adjacent side = 35 units

hypotenuse side = 38 units

Hence,

cos ∅ = 35 / 38

∅ = cos⁻¹ 0.92105263157

∅ = 22.9272842944

∅ ≈ 23 degrees.

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The diameter of the circle is 11.8 units

The circle equation is given as:

(x - 2)^2 + (y + 6)^2 = 35

A circle equation is represented as:

(x - a)^2 + (y - b)^2 = r^2

Where

Diameter = 2r

By comparing both equations, we have

r^2 = 35

Take the square root of both sides

r = 5.9

Multiply by 2

2r = 11.8

Hence, the diameter of the circle is 11.8 units

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The values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4

As  a general rule;

f⁻¹(f(x)) = x

This means that:

f⁻¹(f(6.022)) = 6.022

Also, we have:

f⁻¹(10) + f(-6)

From the table of values, we have:

f⁻¹(10) = -6 and f(-6) =10

So, we have:

f⁻¹(10) + f(-6) = -6 + 10

Evaluate

f⁻¹(10) + f(-6) = 4

Hence, the values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4

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Answer:

$1800

Step-by-step explanation:

Volume of the foundation: 30*12*6 = 2160 cubic feet

we need to convert this into yards because a truckload is 8 cubic yards, 2160/3 = 720 cubic yd

One truckload is 8 cubic yards

# of truckloads needed: 720/8 = 90 truckloads

Cost: $20*90 = $1800

i. P(A) = 0. 4

ii. P(AB) = 0. 9

iii. P(A∩B) =0. 25

From the information given,

Universal set = 40% + 50% + 25% = 0.40 + 0. 50 + 0. 25

A = Mechanical defects = 40%

B = Electrical defects = 50%

A∩B =25%

i. Probability of A , P(A)

= [tex]\frac{40}{100}[/tex]

= [tex]0. 4[/tex]

ii. Probability of B, P(AB)

= [tex]\frac{40}{100} + \frac{50}{100}[/tex]

= [tex]0. 4 + 0. 5[/tex]

= [tex]0. 9[/tex]

iii. Probability of A∩B entails the common factor between A and B

P(A∩B)  = [tex]\frac{25}{100}[/tex] = [tex]0. 25[/tex]

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Answer:

[tex]15x^3 +10x^2 - 15x[/tex]

Step-by-step explanation:

Hello!

Use the distributive property and multiply like terms.

The simplified form is [tex]15x^3 +10x^2 - 15x[/tex].

Answer:

Step-by-step explanation:

Answer:

The equation of the line passing through the points (3,7) and (-2,5) is y=⅖x+29/5

Step-by-step explanation:

Greetings !

[tex]first \: find \: the \: slope \: m \\ m = \frac{(Y₂-Y₁)}{(X₂-X₁)} ..substitute \: vlues \\ m = \frac{(5 - 7)}{( - 2 - 3)} = \frac{ - 2}{ - 5} = \frac{2}{5} \\ y = mx + b \: to \: find \: equation \: of \: aline \\ between \: two \: poins and \: use \: \\ one \: of \: the \: two \: points \: lets \: take( - 2.5) \\ y = mx + b \\ 5 = \frac{ - 2}{5} ( - 2) + b \\ 5 = \frac{ - 4}{5} + b \\ 5 + { - 4}^{5} = b \\ \frac{25 + 4}{5} = b \\ b = \frac{29}{5} \\ finally \: equation \: of \: the \: line \: will \: be \\ y = \frac{2}{5} x + \frac{29}{5} [/tex]

The total repayment made, including principal and interest is $1262.27

The formula for calculating the compound interest is calculated as shown below;

A = P(1+r)^t

where

P is the principal = $1100

rate = 3.5% = 0.035

time "t" =4 years

Substitute

A. = 1100(1+0.035)^4
A = 1100(1.035)^4
A = 1100(1.14752)

A = 1262.27

Hence the total repayment made, including principal and interest is $1262.27

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Step-by-step explanation:

Let take the first derivative

[tex] \frac{d}{dx} ln(x)) = x {}^{ - 1} [/tex]

The second derivative

[tex] - {x}^{ - 2} [/tex]

The third derivative

[tex]2 {x}^{ - 3} [/tex]

The fourth derivative

[tex] - 6 {x}^{ - 4} [/tex]

The fifth derivative

[tex]24 {x}^{ - 5} [/tex]

Let create a pattern,

The values always have x in it so

our nth derivative will have x in it.

The nth derivative matches the negative nth power so the nth derivative so far is

[tex] {x}^{ - n} [/tex]

Next, lok at the constants. They follow a pattern of 1,2,6,24,120). This is a factorial pattern because

1!=1

2!=2

3!=6

4!=24

5!=120 and so on. Notice how the nth derivative has the constant of the factorial of the precessor

so our constant are

[tex](n - 1)[/tex]

So far, our nth derivative is

[tex](n - 1)!x {}^{ - n} [/tex]

Finally, notice for the odd derivatives we are Positve and for the even ones, we are negative, this means we are raised -1^(n-1)

[tex] - 1 {}^{n -1} (n - 1) ! {x}^{-n} [/tex]

That is our nth derivative

The equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6

From the given table, we see that the x-intercepts are;

(-3, 0), (1, 0) and (2, 0)

Now, we are told the the x-intercepts have a multiplicity of one which means they occur as roots only once. Thus, we can say that the roots in factor form are;

(x + 3), (x - 1), (x - 2)

Then, the polynomial will be;

h(x) = (x + 3) * (x - 1) * (x - 2)

h(x) = (x + 3)(x² - 3x + 2)

h(x) = x³ + 3x² - 3x² - 9x + 2x + 6

h(x) = x³ - 7x + 6

Thus, the equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6

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Using the normal distribution, it is found that 0.4068 of crocodiles live between 17.5 and 20.5 years.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as follows:

[tex]\mu = 18, \sigma = 2.6[/tex]

The proportion of crocodiles live between 17.5 and 20.5 years is the p-value of Z when X = 20.5 subtracted by the p-value of Z when X = 17.5, hence:

X = 20.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{20.5 - 18}{2.6}[/tex]

Z = 0.96

Z = 0.96 has a p-value of 0.8315.

X = 17.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{17.5 - 18}{2.6}[/tex]

Z = -0.19

Z = -0.19 has a p-value of 0.4247.

0.8315 - 0.4247 = 0.4068

0.4068 of crocodiles live between 17.5 and 20.5 years.

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Given the diameter of the circular garden, the area of the garden is 28.36 yd².

The area of a circle is expressed as; A = πr²

Given that;

A = πr²

A = 3.14 × (3yd)²

A = 3.14 × 9yd²

A = 28.36 yd²

Given the diameter of the circular garden, the area of the garden is 28.36 yd².

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The monthly payments for each add-on interest loan is $29.7.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

According to the question,

Principal (P) = $1150

Rate of Interest(R) = 6%

Time (T) = 4 years

The interest is calculated as follows:

SI = (P × R × T)/100

SI = (1150 × 6 × 4)/100

SI=$ 276

Amount (A) = P + SI

A = $(1150 +276)

A = $1426

Monthly payment with interest = A/(4×12)

= $ 1426/48

= $29.7

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Answer:

the ansqer is g(x) = 4^x-4 + 2

Answer:

6

Step-by-step explanation:

The equation for this problem would be c = (20 + 8) / 2 - 8. Add 20 and 8 to get 28, divide 28 by 2 to get 14, then subtract 8 to get 6.

Answer:

  8

Step-by-step explanation:

The definition of an average can be used with the given values to write an equation for the number of boys.

The average is the total divided by the number. If there were n original boys, the total was T, where ...

  T/n = 145   ⇒   T = 145n

Adding two boys with an average of 160 cm height, the new total became (T +2(160)) and the new average became ...

  (T +2(160))/(n +2) = 148   ⇒   T = 148(n +2) -320

Equating the values of T, we have ...

  T = 145n = 148(n +2) -320

Solving for n, we find ...

  0 = 3n -24 . . . . . . . . . . . . subtract 145n and simplify

  0 = n -8 . . . . . . . . . . . divide by 3

  8 = n . . . . . . . . . . . add 8

The number of boys in the group at first was 8.

Based on the Venn diagram with results from the travel agency and the popular cities to visit, the following are true:

The Venn diagram shows that the number of people who chose Orlando alone are 5 people namely: John, Michael, Angel, Andrew, and Sally.

Only one customer in the person of Jordan preferred New York and Los Angeles.

2 people liked Orlando and New York only and they were Luke and Robert.

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Answer:

Step-by-step explanation:

Given inequalities below and we are looking for a pair with no solution.

Let's verify:

A) x > 3 and x < 2,

B) x > - 3 and x < - 2,

C) x > - 3 and x < 2,

D) x > - 3 and x > - 2,

At x=0

At x=5

At x=10

The probability that a person chosen at random have run a red light in the past year is 0.45.

Given that 150 people have responded yes and 185 have responded no in a group of people when they asked whether they have run a red light.

Probability lies between 0 and 1. The value of probability can be find by :

Probability= Number items/total items.

Number of people who said that they have run red light=150

Number of people who said that they have not run red light=185

Total people=150+185

=335 people

Probability that a person chosen at random have run red light in the past year=

=Number of people who said that they have run red lights / total people

=150/335

=0.447

After rounding off it will be 0.45.

Hence the probability that a person chosen at random have run a red light in the past year is 0.45.

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Answer: I don't know what you are talking about, but if x is the area, then the answer is 1,210.

Step-by-step explanation: 44 x 55 x 1/2 = 1,210. The formula for the area of a triangle is 1/2 times length times height. Therefore, x = 1,210

Hope this helps.

Answer:

Second option

Step-by-step explanation:

As its a solid line, it indicates the inequality contains equal to in it. As the line crosses the x - axis it must be an option whereby x > or x < . Now read the value which is 7 therefore x ≤ 7

Answer: The largest common factor of 28 and 32 is 4.

Step-by-step explanation:

The factors of 28 are 1, 2, 4, 7, 14, 28

The factors of 32 are 1, 2, 4, 8, 16, 32