A wire that is 76 feet long needs to be divided into lengths using the ratio 1 to 13. What is the longer length? Round your answer to two decimal places if necessary.

Answer:

[tex] x = 16 [/tex]

Step-by-step explanation:

x = length of diagonal, can be calculated using the Law of Cosines as explained below:

a² = b² + c² - 2bc(cosA),

Where,

a = x

b = 17

c = 13

A = 64°

Plug in the values into the formula:

[tex] x^2 = 17^2 + 13^2 - 2(17)(13)*cos(64) [/tex]

[tex] x^2 = 289 + 169 - 442*0.4384 [/tex]

[tex] x^2 = 458 - 193.77 [/tex]

[tex] x^2 = 264.23 [/tex]

[tex] x = \sqrt{264.23} [/tex]

[tex] x = 16.255 [/tex]

Length of diagonal, [tex] x = 16 [/tex] (to nearest whole number)

Answer:

Movies: x gig

pictures: x/2 gig

music:  10 - x - x/2 = 10 - (3/2)x

The amount of gigabytes of music stored on the computer is:

[tex]y = 5 - x[/tex]

In which x is the amount stored in movies.

We solve this question representing the amount of music as a variable, that I will call y.

The total amount of data is 10 gigabytes.

Division of the 10 gigabytes:

Half in pictures, that is, 10/2 = 5 gigabytes.

x are movies.

The rest, y, are music.

Thus, since the sum of this all is 10, we have that:

[tex]5 + x + y = 10[/tex]

[tex]y = 10 - 5 - x[/tex]

[tex]y = 5 - x[/tex]

Thus, the amount of gigabytes of music stored on the computer is [tex]y = 5 - x[/tex], considering x as the amount of gigabytes of movies stored.

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Answer:

C. 9

Step-by-step explanation:

To find the number we add to complete the square, we do (b/2)², or take b (which is 6), divide by 2 (which gives us 3), then square the result (which gives us 9):

6/2 = 3

3² = 9

Answer: 9

Step-by-step explanation: To complete the square, we need a number to create a perfect square trinomial on the left side of the equation.

So the question is, what is that number?

Well it comes from a formula.

The number that we will need to complete the square will always

come from half the coefficient of the middle term squared.

In this case, that's half of 6 which is 3, squared, which is 9.

So we add 9 to both sides of the equation.

This will now allow the left side of the equation to factor.

Answer:

probability that all of the sprinklers will operate correctly in a fire: 0.0282

Step-by-step explanation:

In order to solve this question we will use Binomial  probability distribution because:

A binomial distribution is a probability of a success or failures outcomes in an  repeated multiple or n times.

Number of outcomes of this distributions are two.

The formula is:

b(x; n, P) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]

b = binomial probability  also represented as P(X=x)

x =no of successes

P = probability of a success on a single trial

n = no of trials

[tex]C_{n,x}[/tex] is calculated as:

[tex]C_{n,x}[/tex] = n! / x!(n – x)!

        = 10!  / 10!(10-10)!

        = 1

According to given question:

probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.

number of trials i.e. n = 10 as number of sprinklers are 10

To find: probability that all of the sprinklers will operate correctly in a fire

X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them

So putting these into the formula:

P(X=x) = [tex]C_{n,x}*p^{x} * (1 - p)^{n-x}[/tex]

           = C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰

           =  1 * 0.0282 * (0.3) ⁰

           = 1 * 0.0282 * 1

  P(X=x)        = 0.0282

Answer:

D. is used to reveal an underlying pattern in the data.

Step-by-step explanation:

Smoothing a time series is achieved when a computer uses some pre-programmed calculation methods to remove noise from large volumes of data. Smoothing helps a user detect patterns in a set of data, thus making it possible to make future predictions. For example, smoothing can be used in the prediction of the rise and fall of stock prices. This helps the traders to have an idea of what to expect in the cost of trading.

Although smoothing reveals the patterns in a set of data, it provides no explanation as to why it is so. It is left to the researcher to draw conclusions as to the reasons for the patterns.

Answer:

[tex]\sqrt[4]{xy^3}[/tex].

Step-by-step explanation:

[tex]\sqrt[8]{x^2y^6}[/tex]

= [tex]x^{\frac{2}{8} } y^{\frac{6}{8}}[/tex]

= [tex]x^{\frac{1}{4} } y^{\frac{3}{4}}[/tex]

= [tex]\sqrt[4]{xy^3}[/tex].

Hope this helps!

Answer:

the solution to the problem is D

She can either have 24 people since there are more slices of pizza there will be extras

Answer:

We can see that for this case the vertex is [tex] V= (0,0)[/tex]

The values for a and b are:

[tex] a = \sqrt{169}=13, b= \sqrt{25}=1[/tex]

Then the ellipse have the major axis on x.

In order to find the two foci we need to use the following formula:

[tex] c =\sqrt{a^2 -b^2}[/tex]

And replacing we got:

[tex] c =\sqrt{169-25}= \pm 12[/tex]

And then the two foci are (12,0) and (-12,0)

And the covertex are on this case (-13,0) (13,0) and (0,5) (0,-5) on the y axis

Step-by-step explanation:

For this problem we have the following equation given:

[tex]\frac{x^2}{169} + \frac{y^2}{25}= 1[/tex]

If we compare this with the general expression of an ellipse given by:

[tex] \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}= 1[/tex]

We can see that for this case the vertex is [tex] V= (0,0)[/tex]

The values for a and b are:

[tex] a = \sqrt{169}=13, b= \sqrt{25}=1[/tex]

Then the ellipse have the major axis on x.

In order to find the two foci we need to use the following formula:

[tex] c =\sqrt{a^2 -b^2}[/tex]

And replacing we got:

[tex] c =\sqrt{169-25}= \pm 12[/tex]

And then the two foci are (12,0) and (-12,0)

And the covertex are on this case (-13,0) (13,0) and (0,5) (0,-5) on the y axis

Answer:

54.5 years.

Step-by-step explanation:

From the above question, we are asked to find the time

The formula for Time(t) =

t = log(A/P) / n[log(1 + r/n)]

A = Amount accumulated after a particular interest and period of time = $80,000

P = Principal (Money invested) = $4,000

r = rate = 5.5% = 0.055

n = compounding frequency = compounding continuously

n = number of days in a year × number of hours in a day

= 365 days × 24 hours = 8760

t = log(A/P) / n[log(1 + r/n)]

t = log(80,000/4,000) /8760[log(1 + 0.055/8760)]

t = log(80000 ÷ 4000) ÷ (8760 × [log(1 + 0.0000062785)]

t = 54.468367222 years

Approximately to the nearest tenth of a year, therefore, the length of time it will it take for his money to reach $80,000 is 54.5 years

Answer:

54.5

Step-by-step explanation:

the bag is 200g

total weight with oranges is 1400g

deduct the bags weight from total weight

1400 - 200

1200g

this is the weight of the three oranges

so each orange would be

1200 ÷ 3

400g

Answer:

x = 8 ± 2i[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given

x² - 16x + 60 = - 12 ( subtract 60 from both sides )

x² - 16x = - 72

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 8)x + 64 = - 72 + 64, thus

(x - 8)² = - 8 ( take the square root of both sides )

x - 8 = ± [tex]\sqrt{-8}[/tex] = ± 2i[tex]\sqrt{2}[/tex] ( add 8 to both sides )

x = 8 ± 2i[tex]\sqrt{2}[/tex]

The solution of the given expression is ±2√2i+8

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that

x² - 16x + 60 = - 12

Then subtract 60 from both sides;

x² - 16x = - 72

To complete the square then add ( half the coefficient of the x- term )² to both sides

x² + 2(- 8)x + 64 = - 72 + 64,

(x - 8)² = - 8 ( take the square root of both sides )

x =  ±2√2i+8

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Answer:

C

Step-by-step explanation:

I suppose you have learned that for the sides of a triangle to work, it has to be a + b > c, the 4 is the a, the 8 is the b, the 12 is the c.

So: 4 + 8 > 12; however this is not true, they are equal so the triangle wont be a triangle, it would be lines that never connect.

Answer:

Net present value is $61,058.

Step-by-step explanation:

Net present value is the difference between present value of cash inflows and the present value cash outflows over the period of time. NPV method is used in capital budgeting to analyze profitability of the project.

Less: initial cost is $29,000

Add: Year 1: Cost saving due to new furnace is $5,600 (2,800 oil gallons * $ 2 per gallon)

Year 2: Cost saving due to new furnace is $7,000 (2,800 oil gallons * $ 2.50 per gallon)

Year 3- 20: Cost saving due to new furnace is $8,400 (2,800 oil gallons * $ 3 per gallon)

Less : Maintenance expenditure is $1,200

The furnace will benefit for 20 years and the price per gallon will increase by $0.50 year.

The annuity factor is applied at discount factor of 6% and then present value of each cash inflow and outflow is calculated. The net present value is $61,058.

Hi there! Thanks for your questions ;)

The answers are quite easily, go through the steps below so that you can catch it up yourself!!

= [tex]\rm{sin (x) = \dfrac{9}{20}}[/tex]

= [tex]\rm{0.45}[/tex]

= [tex]\rm{x = arcsin(0.45)}[/tex]

= [tex]\rm{h = 20 \times cos(x)}[/tex]

= [tex]\rm{20 \times cos(26.74)}[/tex]

Hope it is helpful!

Answer:

A(t) = 41,47 in²

Step-by-step explanation:

Let´s call "x" the cut of point to get to pieces of wire, we make a square from x and the regular octagon will be shaped with 24-x

Then Area of the square  A(s)  =  x²

Area of the octagon is  A(o)  = 1/2*p*length of apothem (d)

p = ( 24 - x )

length of apothem (d) :

The side of the octagon is equal to ( 24 - x ) / 8 half the side is  

( 24  -  x ) / 16

tan α  = ( 24- x ) 16 / d      since ∡s in octagon are 360 / 8  = 45°

α ( ∡ between apothem and one of the interiors ∡ of the octagon )half of 45 is  α = 22,5°  

tanα = 0,41

d = (24 - x ) / 16*0,41        d = ( 24 - x ) / 6,56

Then

A(t) = A(s) + A(o)

A(t) =  x²  + (1/2)* ( 24 - x ) ( 24 - x ) / 6,56

Note  A(t) = A(x)

A(x) =  x²  + (1/2) * (24 - x )²/ 6,56

A(x) = x² + ( 1/ 2*6,56) * ( (24)² -48*x + x² )

Taking derivatives on both sides of the equation

A´(x) = 2*x + ( 1/13,12)* ( - 48 + 2x )

A´(x) = 2*x - 48/ 13,12 + 2*x

A´(x) = 4*x - 3,66

A´(x) = 0     4x = 3,66        x  = 0,91 in    and  d =( 24 - x ) / 6,56

d = ( 24 - 0,91 ) / 6,56        d = 3,52

Then  A(s) = (0,91)²      A(s) = 0,83 in²

A(o) = 1/2 * ( 24 - 0,91 )* 3,52

A(o) = 40,63 in²

A(t) = 40,63 + 0,83

A(t) = 41,47 in²

Answer:

The growth rate is of 0.085 = 8.5% a year.

Step-by-step explanation:

General growth equation:

[tex]B(t) = B(0)(1+r)^{t}[/tex]

In which B(t) is the population of butterflies after t years, B(0) is the initial population and r is the growth rate, as a decimal.

We have:

[tex]B(t)=137(1.085)^{t}[/tex]

Comparing to the general equation, we have that:

[tex]B(0) = 137, 1 + r = 1.085[/tex]

Growh rate:

1 + r = 1.085

r = 1.085 - 1

r = 0.085

The growth rate is of 0.085 = 8.5% a year.

Answer: The second option;  y =  (x - a)^2*(x-b)^4

Step-by-step explanation:

Ok, we have that a and b are real numbers different than zero.

In the graph, we can see that the line touches the x-axis in two values. Now, if we would have an equation like:

y = x*(x - a)^3*(x - b)^3

then when x = 0 we would have:

y = 0*(0-a)^3*(0-b)^3 = 0

But in the graph, we can see that when x = 0, the value of y is different than zero, so we can discard options 1 and 3.

So the remaining options are:

y = (x - a)^2*(x-b)^4

y = (x - a)^5*(x - b)

Now, another thing you can see in the graph is that it is always positive.

Particularly the second option allows negative values for y because it has odd powers, then we can also discard this option.

(For example, if x > a and x < b we would have a negative value for y)

Then the only remaining option is y =  (x - a)^2*(x-b)^4

Answer:

B.y =  (x - a)^2*(x-b)^4

Step-by-step explanation:

EDGE 2020 Brainliest please

Please find attached

thank you

The area of Integral is 19 sq units.

An integral in calculus is a mathematical concept that can be used to represent an area or an expanded version of an area. The basic components of calculus are integrals and derivatives. The terms antiderivative and primal are additional terms for integral.

In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).

Given:

∫ 3 0 | 8 x − 10 | d x

Now, the graph touches the x axis  

when 8x- 10 = 0

x= 10/8

x= 5/4

and, When x = 0, y = 10.

So, the limit range will be x = 0 to x = 5/4.

Now, Area of First triangle

= 10 x 5/4 x 1/2

= 25/4

and, Area of second triangle

= 14 x (3- 10/8) x 1/2

= 7 x 7/4

= 49/4

Hence, the total Area = 25/4 + 49/4 = 19 sq. units

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Answer:

Option (D)

Step-by-step explanation:

Zero of any function is defined by the x-value of the function when y = 0.

Let the equation of the line given in the graph is,

y = mx + b

where m = slope of the line

b = y-intercept of the line

Slope of a line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by the formula,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

If the passes through (0, -3) and (-2, 0)

m = [tex]\frac{-3-0}{0+2}[/tex]

m = [tex]-\frac{3}{2}[/tex]

Fro the graph,

y-intercept 'b' = -3

Therefore, equation of the line is,

[tex]y=-\frac{3}{2}x-3[/tex]

For y = 0,

[tex]0=-\frac{3}{2}x-3[/tex]

[tex]\frac{3}{2}x=-3[/tex]

x = -2

Therefore, option (D) will be the answer.

Answer:

d- -2

Step-by-step explanation:

Answer:

∠CAB ≅ ∠SAB is not true

Step-by-step explanation:

CPCTC means id ABC = XYZ, than A=X, AB=XY, C=Z and so on. Basically the number numbers that come in the same order as the other one is equal.

So ∠CAS ≅ ∠BAS is true but ∠CAB ≅ ∠SAB is not.

Hope this helps. If you have any follow-up questions, feel free to ask.

Have a great day! :)

Answer:

sap

Step-by-step explanation:

Incomplete question. I've made some assumptions to provide clarity.

Answer:

a. $45,743.07

b. $44,843.07

Step-by-step explanation:

Let's assume Victor is a single filer with an income of $100,000.

Using the 2017 tax bracket rates for single filers, Victor would be expected to pay:

- 10 percent on the first $9,325 = 10% x 9525 =$932.5

- plus 15 percent of the amount between $9,326 and $37,950 (37950-9326) x 15% = $4293.6

- plus 25 percent of the amount between $37,951 and $91,900 (91900-37,951 ) x25% = $13487.25

- plus 28 percent of the amount over $91,901-$191,650 (191650-91901) x 28% = 27929.72

Total=  $46,643.07

Minus $900 tax credit= $46,643.07-$900= $45,743.07

Minus $900 charitable contribution = $45,743.07-$900= $44,843.07

Answer:

work is shown and pictured

Answer:

Image is attached.

Answer:

You need to add 150 mL of 65% alcohol solution.

Step-by-step explanation:

You have 300 mL of 20% solution.

300 mL of 20% alcohol solution has 20% * 300 mL of alcohol.

You have 65% solution.

Let the volume of 65% solution you add be x.

In 65% solution, 65% of the volume is alcohol, so the amount of alcohol in x amount of 65% solution is 65% * x.

You want 35% solution.

The total amount of 35% solution you will make is 300 mL + x. The amount of alcohol in that amount of solution is 35% * (x + 300).

Equation of alcohol content:

20% * 300 + 65% * x = 35% * (x + 300)

60 + 0.65x = 0.35x + 105

0.3x = 45

x = 150

Answer: You need to add 150 mL of 65% alcohol solution.

Assuming angle A is opposite to side a, B is the opposite to side b, and angle C is the opposite to side c.

Answer:

The right triangle has the following angles:

A = 48.31º, B = 41.69º and C = 90º.

The sides are:

[tex] \\ a = 37.26[/tex], [tex] \\ b = 33.12[/tex] and c = 49.9.

Step-by-step explanation:

The inner sum of a triangle = 180º.

A=48.31º,

C=90º

A + B + C = 180º

48.31º+ B + 90º = 180º

B = 180º - 90º - 48.31º

B = 41.69º

We can apply the Law of Sines to solve for unknown sides:

[tex] \\ \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]

We know that sin(90º) = 1.

[tex] \\ \frac{a}{sin(48.31)} = \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]

Then, a is:

[tex] \\ \frac{a}{sin(48.31)} = \frac{49.9}{1}[/tex]

[tex] \\ a = 49.9*sin(48.31)[/tex]

[tex] \\ a = 49.9*0.7467[/tex]

[tex] \\ a = 37.26[/tex]

Thus, b is:

[tex] \\ \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]

[tex] \\ b = 49.9*sin(41.69)[/tex]

[tex] \\ b = 33.12[/tex]

Answer:

We conclude that the population means checkout times of the two new systems differ.

Step-by-step explanation:

We are given the result in the following summary of the data;

System          System B

n1=120             n2=100

x1=4.1 min       x2=3.4 min

σ1=2.2 min     σ2= 1.5 min

Let [tex]\mu_1[/tex] = population mean checkout time of the first new system

[tex]\mu_2[/tex] = population mean checkout time of the second new system

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex]      {means that the population mean checkout times of the two new systems are equal}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex]      {means that the population mean checkout times of the two new systems differ}

The test statistics that will be used here is Two-sample z-test statistics because we know about population standard deviations;

                          T.S.  =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1} + \frac{\sigma_2^{2} }{n_2}} }[/tex]  ~ N(0,1)

where, [tex]\bar X_1[/tex] = sample mean checkout time of the first new systems = 4.1 min

[tex]\bar X_2[/tex] = sample mean checkout time of the second new systems = 3.4 min

[tex]\sigma_1[/tex] = population standard deviation of the first new systems = 2.2 min

[tex]\sigma_2[/tex] = population standard deviation of the second new systems = 1.5 min

[tex]n_1[/tex] = sample of the first new systems = 120

[tex]n_2[/tex] = sample of the second new systems = 100

So, the test statistics =  [tex]\frac{(4.1-3.4)-(0)}{\sqrt{\frac{2.2^{2} }{120} + \frac{1.5^{2} }{100}} }[/tex]  

                                    =  2.792

The value of z-test statistics is 2.792.

Now, at 0.05 level of significance, the z table gives a critical value of -1.96 and 1.96 for the two-tailed test.

Since the value of our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the population mean checkout times of the two new systems differ.

Answer:

[tex](x + {y}^{2}) = {x}^{2} + 2x {y}^{2} + {y}^{4} [/tex]

Thanks!!!!

Answer:

4.2 in

Step-by-step explanation:

let us first visualize the sail as a triangular shape

the angle of the triangle from top is 40°

the height of the triangle is give as 5 in

we can apply SOH CAH TOA to solve for the base of the sail

the opposite = the base of the sail

the adjacent = the height of the sail= 5 in

therefore

Tan∅= Opp/Adj

Tan(40)= Opp/5

Opp= Tan(40)*5

Opp= 0.8390*5

Opp= 4.195 in

Hence the width of the sail is 4.2 in to the nearest tenths

Answer:

4.2

Step-by-step explanation:

Answer:

There is a solution. The ordered pair is (4, 2).

Step-by-step explanation:

Solve the system of equations by using the substitution method.

[tex]x+y=6\\x=2y[/tex]

Substitute x as 2y in the first equation and solve for y.

[tex]2y+y=6\\ 3y=6\\(3y)/3=6/3\\y=2[/tex]

Substitute y as 2 in the second equation and solve for x.

[tex]x=2(2)\\x=4[/tex]

Answer: 24 because you add 5 for every number ex: 9+5=14

Answer:

24

Step-by-step explanation:

The difference can be calculated by subtracting the second term with the first term.

d = 14 - 9

d = 5

The difference is 5.

Add 5 to 19.

19 + 5 = 24