If a person invested half of her money at 9% and half at 7% and received $160 interest, find the total amount of money invested.

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:

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:

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:

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:

yep it's D

Step-by-step explanation:

Answer: A) 0

P(A and B) = 0 when events A and B are disjoint, aka mutually exclusive.

We say that two events are mutually exclusive if they cannot happen at the same time. An example would be flipping a coin to have it land on heads and tails at the same time.

Answer:

Option (2)

Step-by-step explanation:

If a perpendicular is drawn from the center of a circle to a chord, perpendicular divides the chord in two equal segments.

By using this property,

Segment MN passing through the center Q will be perpendicular to chords HI ans GJ.

By applying Pythagoras theorem in right triangle KNJ,

(KJ)² = (KN)² + (NJ)²

(33)² = (6√10)² + (NJ)²

NJ = [tex]\sqrt{1089-360}[/tex]

NJ = [tex]\sqrt{729}[/tex]

    = 27 units

Since, GJ = 2(NJ)

GJ = 2 × 27

GJ = 54 units

Option (2) will be the answer.

Answer:

Step-by-step explanation:

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:

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:

8192

Step-by-step explanation:

2 cells at beginning, so the equation is (2)*(2^(4t)) where t is in hours. At the end of 3 hours, the cells will be 2*(2)^(12)=8192

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%

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.

Answer:

A. has a constant proportion of 1/4.

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

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Given that a random variable X is normally distributed with a mean of 2 and a variance of 4, find the value of x such that P(X < x)=0.99   using the cumulative standard normal distribution table

Answer:

6.642

Step-by-step explanation:

Given that mean = 2

standard deviation = 2

Let X be the random Variable

Then X [tex]\sim[/tex] N(n,[tex]\sigma[/tex])

X [tex]\sim[/tex] N(2,2)

By Central limit theorem;

[tex]z = \dfrac{X - \mu}{\sigma} \sim N(0,1)[/tex]

[tex]z = \dfrac{X - 2}{2} \sim N(0,1)[/tex]

P(X<x) = 0.09

[tex]P(Z < \dfrac{X-\mu}{\sigma })= 0.99[/tex]

[tex]P(Z < \dfrac{X-2}{2})= 0.99[/tex]

P(X < x) = 0.99

[tex]P(\dfrac{X-2}{2}< \dfrac{X-2}{2})=0.99[/tex]

[tex]P(Z< \dfrac{X-2}{2})=0.99[/tex]

[tex]\phi ( \dfrac{X-2}{2})=0.99[/tex]

[tex]( \dfrac{X-2}{2})= \phi^{-1} (0.99)[/tex]

[tex]( \dfrac{X-2}{2})= 2.321[/tex]

X -2 = 2.321 × 2

X -2 = 4.642

X = 4.642 +2

X = 6.642

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:

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:

The 2 Gallon Tank is Enough

Step-by-step explanation:

A drink bottler needs to bottle 16 one-pint bottles. He has a 2 gallon tank and a 3 gallon tank.

There are 8 pints in a gallon. This means that 2 gallons would be 16 pints.

[tex]8 * 2 = 16[/tex]

So, the 2 gallon tank has 16 pints, which means that the 2 gallon tank should be enough to bottle all 16 bottles.

Answer:

2 gallon tank

Step-by-step explanation:

16 pints is the same as 2 US gallons

Answer:

slope = 2

Step-by-step explanation:

will make it so simple and short

slope = rise / run

slope = 6 / 3

slope = 2

Answer:

B

Step-by-step explanation:

The formula for slope is (y2-y1)/(x2-x1)

In this case it is (1+5)/(3-0)

6/3

2

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:

w ≥ -18

Step-by-step explanation:

Answer:

w is greater than or equal to-18

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: 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

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

Learn more : https://brainly.com/question/7589262

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]\= 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]

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

Answer:

Length = 21.3333333333;   Width: 12.6666666667

Step-by-step explanation:

Perimeter = 68

Perimeter of a rectangle:

2 (L +W)

Length (L) = 2W - 4

Width = W

2 ( 2W -4 +W) = 68

=> 2 (3W - 4) = 68

=> 6w -8 = 68

=> 6w = 76

=> w = 12.6666666667

Length = (12.6666666667 X 2) - 4

=> 21.3333333333