what is the solution to the system of equations?

y = 4x-10
y=2

A) (3,2)
B) (2,3)
C) (-2,2)
D) (2,-2)

Answer:

Please check if the answer is a = 4 or not

Answer:

There are 23 people in line at 6:00 A.M

Step-by-step explanation:

When you plug in h=1, we get 23 people

h corresponds with the time 6:00 am, as a result there are 23 people in line

The equation represents how many people will come as the hour increases.

23 represents the initial amount of people in line.

(got this from Khan academy too:))

Answer:

h^2 means h²

(h squared)

Step-by-step explanation:

Step 1: Write equation

144 + h² = 225

Step 2: Subtract 144 on both sides

h² = 81

Step 3: Take square root

√h² = √81

h = 9

Answer: THe slope is 2

SO answer d

Step-by-step explanation:

-4X + 2Y = 16 add 4x to the other side so equation is

2y=16+4x divided by 2

y=8+2x

Answer:

The value of  annuity is  [tex]P_v = \$ 7929.9[/tex]

Step-by-step explanation:

From the question we are told that

    The periodic payment is  [tex]P = \$ 250[/tex]

     The  interest rate  is   [tex]r = 5\% = 0.05[/tex]

     Frequency at which it occurs in a year is  n = 4 (quarterly )

      The number of years is  [tex]t = 10 \ years[/tex]

The  value of the annuity is mathematically represented as

             [tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex] (reference EDUCBA website)

 substituting values

             [tex]P_v = 250 * [1 - (1 + \frac{0.05}{4} )^{-10 * 4} ] * [\frac{(1 + \frac{0.05}{4} )}{ \frac{0.08}{4} } ][/tex]

             [tex]P_v = 250 * [1 - (1.0125 )^{-40} ] * [\frac{(1.0125 )}{0.0125} ][/tex]

             [tex]P_v = 250 * [0.3916 ] * [\frac{(1.0125)}{0.0125} ][/tex]

            [tex]P_v = \$ 7929.9[/tex]

Answer:

75

Step-by-step explanation:

x = 75°

yes x = 75°(OPPOSITE ANGLES ARE EQUAL)

..

Answer:  width = 2.4 in, length = 5

Step-by-step explanation:

The max area of a right triangle is half the area of the original triangle.

Area of the triangle = (6 x 8)/2  = 24

--> area of rectangle = 24 ÷ 2 = 12

Next, let's find the dimensions.

The length is adjacent to the hypotenuse. Since we know the area is half, we should also know that the length will be half of the hypotenuse.

length = 10 ÷ 2 = 5

Use the area formula to find the width:

A = length x width

12 = 5 w

12/5 = w

2.4 = w

The dimensions of the rectangle with greatest area is length is 3 inch and the width is 4 inch.

Let the length and width of the rectangle be x and y.

Then Area of the rectangle = xy

Now, from the triangle we can conclude that

[tex]\frac{6-x}{y} =\frac{6}{8} \\y=8(\frac{6-x}{6} ).[/tex]

Put the value of y in Area we get

[tex]A(x)=x\frac{8}{6} (6-x)\\A(x)=\frac{8}{6}(6x-x^{2} )\\[/tex]

Differentiating it w.r.t x we get

[tex]A'(x)=\frac{8}{6}(6-2x )\\A''(x)=\frac{8}{6}(0-2 )\\A''(x)=\frac{-8}{3}[/tex]

Put A'(x)=0 for maximum /minimum value

[tex]A'(x)=0\\\frac{8}{6}(6-2x)=0\\x=3[/tex]

Now, [tex]A''(3)=-\frac{8}{3} <0[/tex]

Therefore the area of the rectangle is maximum for x=3 inch

Now,

[tex]y=\frac{8}{6} (6-3)\\y=4[/tex]

Thus the dimensions of the rectangle with greatest area is 3 inch by 4 inch.

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Answer:

0.10512

Step-by-step explanation:

Given the following :

Mean number of calls(μ) in 2 hours = 14

2 hours = 60 * 2 = 120 minutes

Average number of calls in 45 minutes :

= (45 / 120) * 14

= 0.375 * 14

= 5.25

Now find P( x ≤ 2) = p(x = 0) + p( x = 1) + p(x = 2)

Using the poisson probability formula:

P(x, μ) = [(e^-μ) * (μ^x)] / x!

Where :

e = euler's constant

μ = 5.25

x = 0, 1, 2

Using the online poisson probability calculator :

P(x, 5.25) = P( x ≤ 2) = p(x = 0) + p(x = 1) + p(x = 2)

P(x, 5.25) = P( x ≤ 2) = 0.00525 + 0.02755 + 0.07232 = 0.10512

Answer:

Measure of angle W + measure of angle Z = 180°

Step-by-step explanation:

The reason is that angles in a straight line add up to 180° and angles at a point add up to 360° (i.e the sum of measure of angles W, X, Y, Z is 360°)

Answer:

D is your answer

Step-by-step explanation:

I have no explanation

Answer:

b. 0.585

Step-by-step explanation:

According to Bayes' theorem:

[tex]P(A|B)=\frac{P(B|A)*P(A)}{P(B)}[/tex]

Let A = Person is infected, and B = Person tested positive. Then:

P(B|A) = 93.9%

P(A) = 5.8%

P(B) = P(infected and positive) + P(not infected and positive)

[tex]P(B) = 0.058*0.939+(1-0.058)*0.041\\P(B)=0.09308[/tex]

Therefore, the probability that a person has the disease given that the test result is positive, P(A|B), is:

[tex]P(A|B)=\frac{0.939*0.058}{0.09308}\\P(A|B)=0.585[/tex]

The probability is 0.585.

Answer:

x=4

Step-by-step explanation:

5x - 17 = -x +7

Add x to each side

5x+x - 17 = -x+x +7

6x -17 = 7

Add 17 to each side

6x-17+17 = 7+17

6x =24

Divide each side by 6

6x/6 = 24/6

x = 4

Answer:

4

Step-by-step explanation:

5x - 17 = -x + 7

Add x on both sides.

5x - 17 + x = -x + 7 + x

6x - 17 = 7

Add 17 on both sides.

6x - 17 + 17 = 7 + 17

6x = 24

Divide both sides by 6.

(6x)/6 = 24/6

x = 4

Answer:se

Step-by-step explanation:

Answer:

(28/33+28 ) *100

Step-by-step explanation:

(28/33+28 ) *100

(28/61)*100

Answer:

it's 2

Step-by-step explanation:

I did it before

Answer:

27°

Step-by-step explanation:

D is 72° because it alternates with B, alternate angles are equal.

2x+72°+2x= 180° because it is a straight line.

4x+72°=180°

4x=108°

x=27°

Answer:

I think it is

Step-by-step explanation:

Answer:

5n√2m^ - 3mn

Step-by-step explanation:

Answer:

4 plants

Step-by-step explanation:

If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4

(8 * 4 is 32)

She will have one dollar left but she can't buy another plant since that's not enough.

Answer:

4 plants

Step-by-step explanation:

Take the amount of money she has and divide by the cost per plant

33/8

The amount is 4 with 1 dollar left over

4 plants

Answer: a) 0.8708, b) 5714, c) 0.000, d) 0.3830

Step-by-step explanation:

(a)

To find P(Z>-1.13):

Since Z is negative, it lies on left hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.3708

So,

P(Z>-1.13) = 0.5 + 0.3708 = 0.8708

(b)

To find P(Z<0.18):

Since Z is positive, it lies on right hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.0714

So,

P(Z<0.18) = 0.5 + 0.0714 = 0.5714

(c)

To find P(Z>8):

Since Z is positive, it lies on right hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.5 nearly

So,

P(Z>8) = 0.5 - 0.5 nearly = 0.0000  

(d)

To find P(| Z | < 0.5)

that is

To find P(-0.5 < Z < 0.5):

Case 1: For Z from - 0.5 to mid value:

Table of Area Under the Standard Normal Curve gives area = 0.1915

Case 2: For Z from mid value to 0.5:

Table of Area Under the Standard Normal Curve gives area = 0.1915

So,

P(| Z | < 0.5) = 2 * 0.1915 = 0.3830

The Probability can be determine using z-Table. The z- table use to determine the area under the standard normal curve for any value between the mean (zero) and any z-score.

(a) The value of [tex]P(z>-1.13)=0.8708[/tex].

(b) The value of  [tex]P(Z < 0.18) = 0.5714[/tex].

(c) The value of [tex]P(Z > 8) = 0.0000[/tex].

(d) The value of [tex]P(| Z | < 0.5) =0.3830[/tex].

Given:

The given condition is [tex]Z\sim N(\mu= 0,\sigma = 1).[/tex]

(a)

Find the value for [tex]P(Z > -1.13)[/tex].

Here Z is less than 1 that means Z is negative. So it will lies it lies on left hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area = 0.3708[/tex].

Now,

[tex]P(Z > -1.13)=0.5 + 0.3708 = 0.8708[/tex]

Thus, the value of [tex]P(z>-1.13)=0.8708[/tex].

(b)

Find the value for [tex]P(Z < 0.18)[/tex].

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area = 0.0714[/tex].

Now,

[tex]P(Z <0.18)=0.5 + 0.0714 = 0.5714[/tex]

Thus, the value of  [tex]P(Z < 0.18) = 0.5714[/tex].

(c)

Find the value for [tex]P(Z >8)[/tex].

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area \approx 0.5[/tex].

Now,

[tex]P(Z >8)\approx0.5 - 0.5 = 0.0000[/tex]

Thus, the value of [tex]P(Z > 8) = 0.0000[/tex].

(d)

Find the value for [tex]P(|Z| <0.05)[/tex].

Here Z is mod of Z, it may be positive or negative. Consider the negative value of Z.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area =0.1915[/tex].

Consider the positive  value of Z.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area =0.1915[/tex].

Now,

[tex]P(|Z| <0.5)=2\times 0.1915 = 0.3830[/tex]

Thus, the value of [tex]P(| Z | < 0.5) =0.3830[/tex].

Learn more about z-table here:

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Answer: The machine depreciates during the fifth year by $4000.

Step-by-step explanation:

Given: The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time.

When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year.

Then, the machine depreciates A(x) during the fifth year as

[tex]A(x) =\int^{5}_1200(x - 8)\ dx\\\\=200|\frac{x^2}{2}-8x|^{5}_1\\\\=200[\frac{5^2}{2}-\frac{1^2}{2}-8(5)+8(1)]\\\\=200 [12-32]\\\\=200(-20)=-4000[/tex]

Hence, the machine depreciates during the fifth year by $4000.

Answer:

The  class width is  [tex]C_w \approx 13[/tex]

Step-by-step explanation:

From the question we are told that

 The  upper class limits is [tex]max = 121[/tex]

  The  lower class limits is  [tex]min = 14[/tex]

   The number of classes is  [tex]n = 8 \ classes[/tex]

The class width is mathematically represented as  

       [tex]C_w = \frac{max - min}{n }[/tex]

substituting values

       [tex]C_w = \frac{121 - 14}{8 }[/tex]

       [tex]C_w = 13.38[/tex]

      [tex]C_w \approx 13[/tex]

Since

Answer:

See the attachment for sketch

Thr region is unbounded

DNE

Step-by-step explanation:

y≤ -2x + 10

The inequality is a straight line and region marked by the inequality. It has no boundaries. The boundaries extend to infinity. So the region is unbounded. Unbounded region has no corner points.

Answer:

160 adults and 80 students

Step-by-step explanation:

With the information from the exercise we have the following system of equations:

Let x = number of students; y = number of adults

I want to maximize the following:

z = 3 * x + 6 * y

But with the following constraints

x + y = 240

y / 2 <= x

As the value is higher for adults, it is best to sell as much as possible for adults.

So let's solve the system of equations like this:

y / 2 + y = 240

3/2 * y = 240

y = 240 * 2/3

y = 160

Which means that the maximum profit is obtained when there are 160 adults and 80 students, so it is true that added to 240 and or every two adults, there must be at least one student.

Answer:

D. The statement is false. Double blinding is used to decrease the placebo effect.

Step-by-step explanation:

In a double blind study, neither researchers nor the participants know which group is receiving the placebo. If the researchers do not know which group took the medication, they cannot influence the behavior of this group, knowingly or nor, by suggesting how they should behave.

Therefore, a​ double-blind experiment is used to decrease the placebo effect.

Answer:

13, 21

Step-by-step explanation:

Add 8 to the next number from the left to the right.

Answer:

The next three numbers in the sequence are: 13, 21, 29.

Step-by-step explanation:

Common Pattern: +8

-27 +8 = -19

-19 + 8 = -11

-3 + 8 = 5

5 + 8 = 13

13 + 8 = 21

21 + 8 = 29

Answer:

The speed of the first train is 70 km/hr

The speed of the second train is 60 km/hr

Step-by-step explanation:

For the first train:

Travel time = 2 hours

The speed = ?

we designate the speed as V

For the second train:

The travel time = 1 hr 15 min = 1.25 hrs (15 minutes = 15/60 hrs)

speed = 10 km/hr slower than that of the first train, we can then say

the speed = V - 10

The total distance traveled by both trains in the opposite direction of one another is 215 km

we can put this problem into an equation involving the distance covered by the trains.

we know that distance = speed x time

the distance traveled by the first train will be

==> 2 hrs x V = 2V

the distance traveled by the second train will be

==> 1.25 hrs x (V - 10) = 1.25(V - 10)

Equating the above distances to the total distance between the trains, we'll have

2V + 1.25(V - 10) = 215

2V + 1.25V - 12.5 = 215

3.25V = 215 + 12.5

3.25V = 227.5

V = 227.5/3.25 = 70 km/hr     this is the speed of the first train

Recall that the speed of the second train is 10 km/hr slower, therefore

speed of the second train = 70 - 10 = 60 km/hr

The speed of the trains are 70km/hr and 60km/hr respectively.

The distance of the first train will be represented by: = 2 × D = 2D

The distance of the second train will be represented by: = 1.25 × (D - 10) = 1.25(D - 10).

Based on the information given in the question, the equation to solve the question will be:

2D + 1.25(D - 10) = 215

Collect like terms

2D + 1.25D - 12.5 = 215

3.25D = 215 + 12.5

3.25D = 227.5

D = 227.5/3.25

D = 70km/hour

The speed of the second train will be:

= 70 - 10 = 60km per hour.

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Answer:

hundreths

Step-by-step explanation:

After the decimal there is tenths, hundreths thousandnths, tens of thousands e.t.c

Answer:

Hello! The answer will be hundredths.

Step-by-step explanation:

The 5 means the thousandths.

The 0 means the hundredths.

The 8 means the tenths.

The 7 means the ones

And the 6 means the tens.

Hope this helps! :)

( below I attached a picture, which might be helpful.)

Answer:

Step-by-step explanation:

Given a sample of seven admission test scores for a professional school listed 11.3, 10.6, 11.7, 9.7, 11.7, 9.5 and 11.7, the mean of the numbers is the sum total of the values divided by the total number of admission test score. The mean is as calculated below.

Mean = {11.3 + 10.6 + 11.7 + 9.7 + 11.7 + 9.5 + 11.7}/7

Mean = 76.2/7

Mean = 10.9

The mean score is 10.9 to 1 decimal place.

Note that the mean does not represent the centre of the data. It represents the average value of the datas. The mean does not represent the center because it is not a data value. The mean will give a value that is different from the values given in the data.

b) The median score is the score in the centre after re-arrangement. The arrangement can either be ascending or descending order. On re-arranging in ascending order;

9.5, 9.7, 10.6, (11.3), 11.7, 11.7, 11.7

After rearranging, it can be seen that the number at the centre of the data is 11.3, hence the median score is 11.3.

The median represents the center

c) The mode is the scores that occurs most. According to the data given, the score that occur most is 11.7. The score occurs the highest number of times (3 times) compare to other scores in the data. Hence, the modal score is 11.7.

The mode(s) does (do) not represent the center because it (one) is the largest data value.

Answer:

x = 1

Step-by-step explanation:

Set up the rational expression with the same denominator over the entire equation.

Since the expression on each side of the equation has the same denominator, the numerators must be equal

5x =4x+1

Move all terms containing x to the left side of the equation.

Hope this can help you

Answer:

the smaller is 9 while the digger is 18

Answer:

after 6 half lives: 210(1/2)^6= 3.28125

Step-by-step explanation:

isotope to be reduced to half its initial mass at first:

210(1/2)=105 half it is original weight

after second life: 210(1/2)^2=105(1/2)=52.5

after third : 210(1/2)^3=52.5/2=26.25

after fourth : 26.25/2=12.125

after fifth : 13.125/2

after 6 half lives: 210(1/2)^6= 3.28125