Solve for h: W = 5h - 90 (must show step by step)

Answer:

yep it's D

Step-by-step explanation:

Answer:

The red arrow shows the resultant vector. We have a Side Angle Side triangle ABC so can use The Cosine Rule:

a2=b2+c2−2bccosA

This becomes:

R2=7002+402−(2×700×40×cos45)

R2=491,600−39,597.9

R=672.3xkm/hr

This is the groundspeed of the aircraft.

To find θ we can use The Sine Rule:

sinCc=sinAa

This becomes:

sinθ40=sin45672.3

sinθ=0.04207

θ=2.41∘

This is known as the drift angle and is the correction the pilot should apply to remain on course.

The heading is the direction the aircraft's nose is pointing which is 000∘.

The track is the actual direction over the ground which is 357.6∘

An alternative method to this would be to separate each vector into vertical and horizontal components and add.

The resultant can be found using Pythagoras.

Start with the slope formula.

m = y2-y1/x2 - x1

We take the second y minus the first y

over the second x minus the first x.

So we have 4 - 6/8 - -4.

This simplifies to -2/12 which reduces to -1/6.

Answer:

The probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is 0.0885.

Step-by-step explanation:

We are given that the population of men at UMBC has a mean height of 69 inches with a standard deviation of 4 inches. The women at UMBC have a mean height of 65 inches with a standard deviation of 3 inches.

A sample of 50 men and 40 women is selected.

The z-score probability distribution for the two-sample normal distribution is given by;

                          Z  =  [tex]\frac{(\bar X_M-\bar X_W)-(\mu_M-\mu_W)}{\sqrt{\frac{\sigma_M^{2} }{n_M}+\frac{\sigma_W^{2} }{n_W} } }[/tex]  ~ N(0,1)

where, [tex]\mu_M[/tex] = population mean height of men at UMBC = 69 inches

           [tex]\mu_W[/tex] = population mean height of women at UMBC = 65 inches

           [tex]\sigma_M[/tex] = standard deviation of men at UMBC = 4 inches

           [tex]\sigma_M[/tex] = standard deviation of women at UMBC = 3 inches

           [tex]n_M[/tex] = sample of men = 50

           [tex]n_W[/tex] = sample of women = 40

Now, the probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is given by = P([tex]\bar X_M-\bar X_W[/tex] > 5 inches)

 P([tex]\bar X_M-\bar X_W[/tex] > 5 inches) = P( [tex]\frac{(\bar X_M-\bar X_W)-(\mu_M-\mu_W)}{\sqrt{\frac{\sigma_M^{2} }{n_M}+\frac{\sigma_W^{2} }{n_W} } }[/tex] > [tex]\frac{(5)-(69-65)}{\sqrt{\frac{4^{2} }{50}+\frac{3^{2} }{40} } }[/tex] ) = P(Z > 1.35)

                                         = 1 - P(Z [tex]\leq[/tex] 1.35) = 1 - 0.9115 = 0.0885

The above probability is calculated by looking at the value of x = 1.35 in the z table which has an area of 0.9115.      

Answer: 3.41x10^3

Step-by-step explanation:

At the beginning of the year, we have:

R = 6.2x10 rats.

And we know that, in one year, each rat produces:

O = 5.5x10 offsprins.

Then each one of the 6.2x10 initial rats will produce 5.5x10 offsprings in one year, then after one year we have a total of:

(6.2x10)*(5.5x10) = (6.2*5.5)x(10*10) = 34.1x10^2

and we can write:

34.1 = 3.41x10

then: 34.1x10^2 = 3.41x10^3

So after one year, the average number of rats is:  3.41x10^3

Answer:

1 square foot is the answer

Answer:

1 ft^2

Step-by-step explanation:

We know 12 inches = 1 ft

12 inches by 12 inches

1 ft by 1 ft

The area is 1 * 1 = 1 ft^2

Answer:

40 mph.

Step-by-step explanation:

Suppose grandma's house is  30 miles away (any distance would do but 30 is convenient).

Speed = distance / time

time = distance / speed

Time to get there =  30/60 = 1/2 hour.

Time to get back = 30/30 = 1 hour

Average speed  = total distance/ total time

=  (30 + 30) / ( 1 + 1/2)

= 60 / 1.5

=  40 miles per hour.

You cannot take the average of the speeds directly

(60+ 30)/2  = 45 is not correct as you cannot average ratios ( speed is a ratio).

Answer:

B

Step-by-step explanation:

What work is there to show? you basically isolate x. add 2 to both sides. and you get x is greater than or equal to 5. So the answer is B.

x-2[tex]\geq[/tex]3

 +2 +2

x[tex]\geq[/tex]5

Answer:

Step-by-step explanation:

Lets, turn this into words and use order of operations, First, we look for multiplication and division.

the sum of one fourth of 5 times of 8 and 10 gets you 1/4(5*8) + 10 = 20

what is the number if 4 is subtracted from the sum

20 - 4 = 16

Answer:

X`= -0.60872 Y + 176.4085

or X`=   176.4085-0.60872 Y

Step-by-step explanation:

Country  Gold Value  Debt (% of GDP)

               ($ billions) X           Y                 XY          X²            Y²

China            63                 17.7              1115.1         3969       313.29

France         146                81.7              11928.2    21316       6674.89

Indonesia    203               83.2            16889.6    41209       6947.2

Germany       33               69.2             2283.6     1089          4788.64

Italy              147                 119              17493       21609        14161

Netherlands   36             63.7              2293.2      1296         4057.69

Russia           50                9.9              495            2500        98.01

Switzerland  62                   55            3410           3844         3025

United States 487             93.2           45,388.2      237169    8686.24      

∑                     1227           592.6          101245.9      334001      48751.96

The estimated regression equation that can be used to predict the debt of a country given the total value of its gold holdings

X =  a1 + bxy Y

wher e

bxy = n ∑XY -∑X∑Y/ n ∑Y²- (∑Y)²

= 9( 101245.9 )-  (1227 *592.6)/  48751.96-(592.6)²

911213.1 - 727120.2/ - 302422.8= - 0.60872

a1= X` -bxy Y`= 136.33- (-0.60872)(65.84)

= 136.33+ 40.07858= 176.4085

Hence X`= -0.60872 Y + 176.4085

or X`=   176.4085-0.60872 Y

Answer:

282.5 inches squared

Step-by-step explanation:

A triangle is half the area of a square.

So we will solve the area as if we were finding the area for a square, and then we halve the result.

Length multiply by height to get the area:

28.25 × 20 = 565 inches squared

Now, half the answer to get the area of the triangle:

565/2=282.5 inches squared

Answer:

87; 2%

Step-by-step explanation:

An exponential growth model is defined as :

F(x) = A( 1 + r)^x

Where;

A = Initial amount,

r = rate of increase

x = time

Comparing the exponential growth function with the exponential growth model given;

f(x)=87(1.02)^x

A = 87 = Initial amount

The growth rate of the model expressed as a percentage :

Taking :

(1 + r) = 1.02

1 + r = 1.02

r = 1.02 - 1

r = 0.02

Expressing r as a percentage :

0.02 * 100% = 2%

Answer:

Step-by-step explanation:

1.)

The price of the house will be 500,000 which will make the downpayment 500,000*.2=100,000

so write down 500,000 and 100,000

2.)

For this one let's do 3 years at 3%

which would make the effective rate .03/12=.0025

let x= monthly payment

[tex]100000=x\frac{(1+.0025)^{12*3}-1}{.0025}[/tex]

which i will round to 2658.12

so write down: 3 years, 3%, [tex]100000=2658.12\frac{(1+.0025)^{12*3}-1}{.0025}[/tex], 2658.12

3.) the remaining 80% = 500,000-100000= 400,000

For this one let's do 6% for 6 years

which would make the effective rate: .06/12= .005

[tex]400000=x\frac{1-(1.005)^{-12*6}}{.005}\\x=6629.155157[/tex]

which i will round to 6629.16

so write down: [tex]400000=6629.16*\frac{1-(1+.005)^{-12*6}}{.005}[/tex], 6629.16

Answer:

A. has a constant proportion of 1/4.

Complete question is;

Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?

Answer:

P(All three are not caused by firmware) = 83.84%

Probability that the entire batch will be accepted = 0.8384

Step-by-step explanation:

We are told that out of the 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware.

Thus,

Cases not caused by firmware = 8834 - 504 = 8330

So, probability of the first case not being affected by firmware is;

P(first case not caused by firmware) = 8330/8834

Also,

Probability of second case not being affected by firmware is given as;

P(second case not caused by firmware|first case not affected by firmware) = 8329/8833

Similarly,

Probability of third case not being affected by firmware is given as;

P(third case not caused by firmware|first and second not caused by firmware) = 8328/8832

Now, looking at the 3 Probabilities gotten, it is obvious that the events are not independent because the probability of occurence of one event depends on the probability of occurence of the other event.

Thus, we will make use of the general multiplication rule which is;

P(A & B) = P(B) × P(A|B)

Thus;

P(All three not caused by firmware) = P(first case not caused by firmware) × P(second case not caused by firmware|first case not affected by firmware) × P(third case not caused by firmware|first and second not caused by firmware)

Plugging in the relevant values, we have;

P(All three not caused by firmware) = (8330/8834) × (8329/8833) × (8328/8832)

P(All three are not caused by firmware) = 0.83840506679 ≈ 83.84%

Explanation: Parallel lines have the same slopes, but different y intercepts.

Answer:

the slope of the red line is also -1/2

Step-by-step explanation:

Answer:

a

  [tex]df = 24.32[/tex]

b

 [tex]df = 30.10[/tex]

c

 [tex]df = 30.7[/tex]

d

[tex]df = 25.5[/tex]

Step-by-step explanation:

Generally degree of freedom is mathematically represented as

          [tex]df = \frac{ [\frac{ s^2_i }{m} + \frac{ s^2_j }{n} ]^2 }{ \frac{ [ \frac{s^2_i}{m} ]^2 }{m-1 } +\frac{ [ \frac{s^2_j}{n} ]^2 }{n-1 } }[/tex]

Considering a

         a) m = 12, n = 15, s1 = 4.0, s2 = 6.0

           [tex]df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{15} ]^2 }{ \frac{ [ \frac{4^2}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{15} ]^2 }{15-1 } }[/tex]

         [tex]df = 24.32[/tex]

Considering b

       (b) m = 12, n = 21, s1 = 4.0, s2 = 6.0

          [tex]df = \frac{ [\frac{ 4^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{4^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }[/tex]

        [tex]df = 30.10[/tex]

Considering c

      (c) m = 12, n = 21, s1 = 3.0, s2 = 6.0

           [tex]df = \frac{ [\frac{ 3^2 }{12} + \frac{ 6^2 }{21} ]^2 }{ \frac{ [ \frac{3^4}{12} ]^2 }{12-1 } +\frac{ [ \frac{6^2}{21} ]^2 }{21-1 } }[/tex]

           [tex]df = 30.7[/tex]

Considering c

        (d) m = 10, n = 24, s1 = 4.0, s2 = 6.0

                [tex]df = \frac{ [\frac{ 4^2 }{10} + \frac{ 6^2 }{24} ]^2 }{ \frac{ [ \frac{4^2}{10} ]^2 }{10-1 } +\frac{ [ \frac{6^2}{24} ]^2 }{24-1 } }[/tex]

               [tex]df = 25.5[/tex]

Answer:

A - 3.3%

Step-by-step explanation:

From the graph

Where x= 0

Amount =$ 450

It shows that$450 is the capital

Then

When x= 3

Amount=$494.55

So interest generated within 3 years

= $494.55-$450

=$ 44.55

When x= 9

Amount = $583.65

So interest generated within 9 years

= $583.65-$450

=$ 133.65

PRT/10= Interest

450*x*3/100= 44.55

1350x= 4455

X= 4455/1350

X= 3.3

So the rate is =3.3%

Answer:

a

   [tex]\= x = 18.5[/tex]  ,  [tex]\sigma = 5.15[/tex]

b

 [tex]15.505 < \mu < 21.495[/tex]

c

 [tex]14.93 < \mu < 22.069[/tex]

Step-by-step explanation:

From the question we are are told that

    The  sample data is  21, 14, 13, 24, 17, 22, 25, 12

     The sample size is  n  = 8

Generally the ample mean is evaluated as

        [tex]\= x = \frac{\sum x }{n}[/tex]

        [tex]\= x = \frac{ 21 + 14 + 13 + 24 + 17 + 22+ 25 + 12 }{8}[/tex]

         [tex]\= x = 18.5[/tex]

Generally the standard deviation is mathematically evaluated as

         [tex]\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}[/tex]

[tex]\sigma = \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}[/tex]

[tex]\sigma = 5.15[/tex]

considering part b

Given that the confidence level is  90% then the significance level is evaluated as

         [tex]\alpha = 100-90[/tex]

         [tex]\alpha = 10\%[/tex]

         [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex]  from the normal distribution table the value is  

     [tex]Z_{\frac{ \alpha }{2} } = 1.645[/tex]

The margin of error is mathematically represented as

      [tex]E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

=>    [tex]E =1.645 * \frac{5.15 }{\sqrt{8} }[/tex]

=>     [tex]E = 2.995[/tex]

The 90% confidence interval is evaluated as

       [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

       [tex]18.5 - 2.995 < \mu < 18.5 + 2.995[/tex]

       [tex]15.505 < \mu < 21.495[/tex]

considering part c

Given that the confidence level is  95% then the significance level is evaluated as

         [tex]\alpha = 100-95[/tex]

         [tex]\alpha = 5\%[/tex]

         [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex]  from the normal distribution table the value is  

     [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

The margin of error is mathematically represented as

      [tex]E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

=>    [tex]E =1.96 * \frac{5.15 }{\sqrt{8} }[/tex]

=>     [tex]E = 3.569[/tex]

The 95% confidence interval is evaluated as

       [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

       [tex]18.5 - 3.569 < \mu < 18.5 + 3.569[/tex]

       [tex]14.93 < \mu < 22.069[/tex]

Answer:

Step-by-step explanation:

1. The sum of one-third of a number and 27

= [tex]\frac{1}{3}\times x +27\\= 1/3x +27[/tex]

2. The product of a number squared and 4

[tex]Let\:the\:unknown\: number\: be \:x\\\\x^2\times4\\\\= 4x^2[/tex]

3.Write a verbal expression for 5n^3 +9.

The sum of the product and of 5 and a cubed number and 9

Answer:

Suppose that the height (in centimeters) of a candle is a linear function of

the amount of time (in hours) it has been burning.

After 11 hours of burning, a candle has a height of 23.4 centimeters.

After 30 hours of burning, its height is 12 centimeters.

What is the height of the candle after 13 hours?

:

Assign the given values as follows:

x1 = 11; y1 = 23.4

x2 = 30; y2 = 12

:

Find the slope using: m = %28y2-y1%29%2F%28x2-x1%29

m = %2812-23.4%29%2F%2830-11%29 = %28-11.4%29%2F19

:

Find the equation using the point/slope formula: y - y1 = m(x - x1)

y - 23.4 = -11.4%2F19(x - 11)

y - 23.4 = -11.4%2F19x + 125.4%2F19

y = -11.4%2F19x + 125.4%2F19 + 23.4

y = -11.4%2F19x + 125.4%2F19 + 23.4

y = -11.4%2F19x + 125.4%2F19 + 444.6%2F19

y = -11.4%2F19x + 570%2F19

y = -11.4%2F19x + 30, is the equation

:

What is the height of the candle after 13 hours?

x = 13

y = -11.4%2F19(13) + 30

y = -148.2%2F19 + 30

y = -7.8 + 30

y = 22.2 cm after 13 hrs

Answer:

b = -9.

Step-by-step explanation:

The line passes through (4, 3) and (7, 12). First, we need to find the slope: the rise over the run.

(12 - 3) / (7 - 4) = 9 / 3 = 3.

Now that we have the slope, we can say that m = 3. So, we have an equation of y = 3x + b. To find b, we can use M(4, 3) and say that y = 3 and x = 4.

3 = 3 * 4 + b

b + 12 = 3

b = -9.

Hope this helps!

The value of b in the equation is -9

The points are given as:

M(4, 3) and N(7, 12)

The equation is then calculated using:

[tex]y = \frac{y_2 -y_1}{x_2 -x_1} * (x - x_1) + y_1[/tex]

This gives

[tex]y = \frac{12 -3}{7 -4} * (x - 4) + 3[/tex]

Evaluate the quotient

y = 3 * (x - 4) + 3

Open the bracket

y = 3x - 12 + 3

Evaluate the difference

y = 3x - 9

Hence, the value of b is -9

Read more about linear equations at:

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Answer:

B

Step-by-step explanation:

the data value of x is 0 the the value would be .75 times that by 2 get 1.25

Answer:

There is a positive correlation between these two variables.

Step-by-step explanation:

Positive correlation is an association amid two variables in which both variables change in the same direction.  

A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.

As the distance covered by the vehicle increases the amount of gas consumed also increases. Thus, the weekly cost of gas will also increase.

Thus, there is a positive correlation between these two variables.

Answer:

infinite solutions along the line y = 2x+1

Step-by-step explanation:

3y – 6x = 3

y = 2x + 1

Replace y in the first equation with the second equation

3 ( 2x+1) -6x =3

6x +3 -6x = 3

3=3

This is always true so there are infinite solutions along the line y = 2x+1

Step-by-step explanation:

Hi, there!!!

you mean to solve it, right.

then let's begin...

3y-6x=3..........epuation 1.

y = 2x+1..........equation 2.

now, substituting the value y of equation 2 in equation 1. so, we get,

3y-6x=3

or, 3(2x+1) -6x = 3

or, 6x+3-6x=3

by simplifying it we get, 3=3

so, this equation can have infinite solution.

you may have wrote wrong question ..

Answer:

The train on the course of moving to the side track has to be moving faster so the trains don't hit eachother.

Step-by-step explanation:

Laws of physics....

Answer: r = 50 miles/h

Step-by-step explanation:

Let r be the rate of average speed.

Then

r = D/t

r = 150/3

r = 50 miles/h

please click thanks and mark brainliest if you like :)

what you're trying to do is form an equation for y

6x + 5y = 10    

5y = -6x + 10         we need y to be singular so divide by numeral before y

y = - 6x/5 + 10/5

y = - 6x/5 + 2

a) The Investment portfolio consisting of the internet fund and Blue chip fund would be the recommended Portfolio for a moderate risk investor

b) The annual return for the portfolio is = $5100 ( Calculated using the excel formula sheet attached below )

The best/recommended investment portfolio for this client is the Investment portfolio consisting of the internet fund and Blue chip Fund because the Portfolio consists of a lower risk rating of 4 for every thousand which is conservative, and also an Internet fund which has a risk rating of 6 for every thousand ( aggressive ). The combination of a high and low risk investment fund in a portfolio results to an average/moderate risk portfolio.

Calculating the Annual return for the portfolio ( using the excel sheet below)

Model                                 Internet fund            Blue chip fund

Amount to invest                  20                                30

Total amount invested = 20 + 30 = 50

Total risk rating = 240

Total return = 5.1  

hence: The recommended investment portfolio for this client is the Blue chip fund and the total return on the portfolio = $5100 applying the excel formulae attached below

Internet Fund = $20,000

Blue chip fund = $30,000

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