Write a real-world situation that could be represented by the system
Y=3x+10
Y=5x+20

Answer:

X=-2or,-3

Step-by-step explanation:

X^2+5x+6=0

or,x^2+(2+3)x+6=0

or,x^2+2x+3x+6=0

or,x(x+2)+3(x+2)=0

or,(x+3) (x+2)=0

Either,

x+3=0 x+2=0

or,x=-3 or,x=-2

Therefore,the value if x is -2 or -3 .

I HOPE IT WILL HELP YOU

Answer: 10units^2

Step-by-step explanation:

You can find the area of the trapezoid by multiplying the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then dividing by 2.

The larger base is 2+2+4=8

so

A=(2+8)*2/2

=10

Answer:

Down below

Step-by-step explanation:

   a. Net income= $100,000 (as given in the question)

   b. Return on equity= (net income)/(shareholder’s equity)

Shareholder’s equity= $400,000

Thus return on equity= 100000/400000 = 0.25  or 25%

   a. Net income= $100000 + 50000 –  12800 (debt interest 8% of     $160000)

= $137,200

b. Return on equity= (net income)/(shareholder’s equity)

= 137200/400000

=0.343  or 34.3%

a. Net Income= $100000 + 50000

= $150000

b. Return on equity= (net income)/(shareholder’s equity)

= 150000/(400000 + 160000)

Where ($560,000) 400000 + 160000 is shareholder’s equity

= 0.27 or 27%

Answer:

  8.5

Step-by-step explanation:

For continuous compounding, the account value formula is ...

  A = Pe^(rt)

where P is the invested amount, r is the annual interest rate, and t is the number of years. We want to find t when ...

  3550 = 2400e^(.046t)

  ln(355/240) = 0.046t

  t = ln(355/240)/0.046 ≈ 8.5

It will take 8.5 years for the value to reach $3550.

Answer: 30 for addition and 2376 for multipaction

Step-by-step explanation: Depending on how what algebraic expression.

Answer:

a)

The probability that both will be hopelessly romantic is  

                                                             P(X = 2)   =  0.0361

b)

The probability that at least one person is hopelessly romantic is

               P( X>1) = 0.3439

Step-by-step explanation:

a)

Given data population proportion 'p' = 19% =0.19

                                                          q  = 1-p = 1- 0.19 =0.81

Given  two people are randomly​ selected

 Given n = 2

Let 'X' be the random variable in binomial distribution

[tex]P(X=r) =n_{C_{r} } p^{r} q^{n-r}[/tex]

The probability that both will be hopelessly romantic is

                   [tex]P(X= 2) =2_{C_{2} } (0.19)^{2} (0.81)^{2-2}[/tex]

                     P(X = 2)   = 1 × 0.0361

The probability that both will be hopelessly romantic is  

                                                             P(X = 2)   =  0.0361

b)

The probability that at least one person is hopelessly romantic is

               P( X>1) = 1-P(x<1)

                            = 1 - ( p(x =0)

                            = [tex]1- 2_{C_{0} } (0.19)^{0} (0.81)^{2-0}[/tex]

                           = 1 - (0.81)²

                           = 1 -0.6561

                           = 0.3439

The probability that at least one person is hopelessly romantic is

               P( X>1) = 0.3439

Answer:

Step-by-step explanation:

Using the formula for finding range in projectile, Since range is the distance covered in the horizontal direction;

Range [tex]R = U\sqrt{\frac{H}{g} }[/tex]

U is the velocity of the arrow

H is the maximum height reached = distance below the bullseye reached by the arrow.

R is the horizontal distance covered i.e the distance of the target from the archer.

g is the acceleration due to gravity.

Given R = 60ft, U = 250ft/s, g = 32ft/s H = ?

On substitution,

[tex]60 = 250\sqrt{\frac{H}{32}} \\\frac{60}{250} = \sqrt{\frac{H}{32}}\\\frac{6}{25} = \sqrt{\frac{H}{32}[/tex]

Squaring both sides we have;

[tex](\frac{6}{25} )^{2} = (\sqrt{\frac{H}{32} } )^{2} \\\frac{36}{625} = \frac{H}{32} \\625H = 36*32\\H = \frac{36*32}{625} \\H = 1.84feet[/tex]

The arrow will hit the target 1.84feet below the bullseye.

Answer:

8.7

Step-by-step explanation:

on edge . You're welcome

Answer:

  7 and 8

Step-by-step explanation:

  54 is between 7^2 = 49 and 8^2 = 64.

The square roots have the same relationship.

  49 < 54 < 64

  √49 < √54 < √64

  7 < √54 < 8

Answer:

1/52

Step-by-step explanation:

Answer:

1.8

Step-by-step explanation:

Answer:

(a) See below

(b) r = 0.9879  

(c) y = -12.629 + 0.0654x

(d) See below

(e) No.

Step-by-step explanation:

(a) Plot the data

I used Excel to plot your data and got the graph in Fig 1 below.

(b) Correlation coefficient

One formula for the correlation coefficient is  

[tex]r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}[/tex]

The calculation is not difficult, but it is tedious.

(i) Calculate the intermediate numbers

We can display them in a table.

   x            y             xy                      x²             y²    

   36       0.22              7.92               1296           0.05

   67        0.62            42.21              4489           0.40

   93         1.00            93.00           20164           3.46

 433        11.8          5699.4          233289        139.24

 887      29.3         25989.1          786769       858.49

1785      82.0        146370          3186225      6724

2797     163.0         455911         7823209    26569

3675   248.0         911400        13505625   61504        

9965   537.81     1545776.75  25569715   95799.63

(ii) Calculate the correlation coefficient

[tex]r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{9\times 1545776.75 - 9965\times 537.81}{\sqrt{[9\times 25569715 -9965^{2}][9\times 95799.63 - 537.81^{2}]}} \approx \mathbf{0.9879}[/tex]

(c) Regression line

The equation for the regression line is

y = a + bx where

[tex]a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\= \dfrac{537.81\times 25569715 - 9965 \times 1545776.75}{9\times 25569715 - 9965^{2}} \approx \mathbf{-12.629}\\\\b = \dfrac{n \sum xy - \sum x \sum y}{n\sum x^{2}- \left (\sum x\right )^{2}} - \dfrac{9\times 1545776.75 - 9965 \times 537.81}{9\times 25569715 - 9965^{2}} \approx\mathbf{0.0654}\\\\\\\text{The equation for the regression line is $\large \boxed{\mathbf{y = -12.629 + 0.0654x}}$}[/tex]

(d) Residuals

Insert the values of x into the regression equation to get the estimated values of y.

Then take the difference between the actual and estimated values to get the residuals.

   x            y       Estimated   Residual

    36        0.22        -10                 10

    67        0.62          -8                  9

    93        1.00           -7                  8

   142        1.86           -3                  5

  433       11.8             19               -  7

  887     29.3             45               -16  

 1785     82.0            104              -22

2797    163.0            170               -  7

3675   248.0            228               20

(e) Suitability of regression line

A linear model would have the residuals scattered randomly above and below a horizontal line.

Instead, they appear to lie along a parabola (Fig. 2).

This suggests that linear regression is not a good model for the data.

Answer:

To compute the probabilities, just divide the number of times a number was landed by the total amount of outcomes.

Spinning 2: 30/120 = 0.25  

Spinning 3: 19/120  = 0.16

Spinning 4:  25/120  = 0.21

Spinning 5:  29/120  = 0.24

Spinning 6:  17/120  = 0.14

Stacy would spin a 6 approximately 0.14*50 = 7 times in 50 tries.

Answer: The area of circle V is 196π ft² (196Pi feet squared)

Step-by-step explanation:

From the equation for area of a circle,

A = πr²

Where A is the area of the circle

r is the radius of the circle

In Circle V, the radius, r of the circle is 14 feet

That is,

r = 14ft

Hence, Area is

A = π × (14ft)²

A = π × 14ft × 14ft

A = 196π ft²

Hence, the area of circle V is 196π ft² (196Pi feet squared)

Answer:

The answer is D on Edge 2020

Step-by-step explanation:

I did the Quiz

Answer:

32/25 walls per gallon.

Step-by-step explanation:

Martin uses 5/8 Of a gallon of paint to cover 4/5 Of a wall

Hence 1 gallon would be 4/5÷5/8=

4/5 × 8/5= 32/25 walls per gallon.

Answer: d) all of the above

Step-by-step explanation:

A Hamiltonian circuit is where you follow the path of the circuit touching EVERY VERTEX only ONE time.

Notice that each path given allows every vertex to be touched and each vertex is touched only once.

Therefore, all the options given are valid paths for a Hamiltonian circuit.

Answer:

26

Step-by-step explanation:

Answer:

Step-by-step explanation:

x • (x - 5) • (x - 7)

Answer:

x(x-5)(x-7)

Step-by-step explanation:

x³ - 12x² + 35x

x(x² - 12x + 35)

x(x-5)(x-7)

Answer:

Option C.

Step-by-step explanation:

Let a point (x, y) has a sequence of transformations,

Option A).

Reflects across x-axis then the coordinates will be,

(x, y) → (x, -y)

Then reflects across the y-axis,

(x, -y) → (-x, -y)

Image (x, y) gets changed to (-x, -y) therefore, point (x, y) doesn't map onto itself.

Option B).

(x, y) rotate 90° counter clockwise about the origin.

(x, y) → (-y, x)

Then reflect across x-axis,

(-y, x) → (y, x)

Since coordinates of the image and the actual are not same therefore, image doesn't map itself.

Option C).

(x, y) when reflected across x-axis,

(x, y) → (x, -y)

Then reflected over the x-axis,

(x, -y) → (x, y)

In this option point (x, y) maps onto itself after these transformations.

Option D).

(x, y) rotated 90°counterclockwise about the origin

(x, y) → (-y, x)

Then translated up by 2 units.

(-y, x) → (-y, x+2)

Therefore, (x, y) gets changed after these transformations and doesn't maps itself.

Option (C) will be the answer.

Answer:

you have it correct the answer is option c

Step-by-step explanation:

Answer:

The coordinates of point A after both transformations becomes (0, 3)

Step-by-step explanation:

Translation 4 units down is equivalent to -4 units in the y direction, therefore, we have;

A(-3, 4), B(6, 4), and C(2, -3) becomes

A(-3, 4 - 4), B(6, 4 - 4), and C(2, -3 - 4) which is A(-3, 0), B(6, 0), and C(2, -7)

Rule on operation on coordinates due to rotation of a triangle 90° clockwise is as follows;

For vertex coordinate, (x, y), we change it to (y, -x)

Therefore, we have the coordinates of the point A(-3, 0) after a rotation of 90° clockwise becomes A(0, 3).

Answer:

y = - 3x + 9    or     (y - 6) = - 3(x - 1)

Step-by-step explanation:

I'm assuming you are looking for the equation of the line.

First, let's find the slope of the line, which we use equation (y1-y2) / (x1-x2)

x1: 1      x2: 2

y1: 6     y2: 3

(6-3) / (1-2) = 3 / -1 = -3

The slope of the line is -3.

The equation for slope-intercept form is y = mx + b, where m is slope and b is the y - intercept.

y = -3x+b

Now substitute a set of points in (any coordinates work). I'll use (1, 6)

6 = -3(1)+b

6 = - 3 + b

b = 9

So our equation in slope intercept form is y = - 3x + 9

You can also write this in point slope form,   (y-y1) = m (x-x1)     m is still slope

(y - 6) = - 3(x - 1)

Answer:

0.5616 = 56.16% probability that at least 91 out of 155 students will pass their college placement exams.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 155, p = 0.59[/tex]

So

[tex]\mu = E(X) = np = 155*0.59 = 91.45[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{155*0.59*0.41} = 6.12[/tex]

Probability that at least 91 out of 155 students will pass their college placement exams.

Using continuity correction, this is [tex]P(X \geq 91 - 0.5) = P(X \geq 90.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 90.5. So

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

[tex]Z = \frac{90.5 - 91.45}{6.12}[/tex]

[tex]Z = -0.155[/tex]

[tex]Z = -0.155[/tex] has a pvalue of 0.4384

1 - 0.4384 = 0.5616

0.5616 = 56.16% probability that at least 91 out of 155 students will pass their college placement exams.

Answer:

i think it's c.)3.5 i may be wrong

Step-by-step explanation:

Answer: 10.5 to 11.5 inches

Answer:

10.5 to 11.5 inches

Step-by-step explanation:

Answer:

At least 832 teenargers must be interviewed.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval

At least n teenargers must be interviewed.

n is found when M = 0.1.

We have that [tex]\sigma = 1.12[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.1 = 2.575*\frac{1.12}{\sqrt{n}}[/tex]

[tex]0.1\sqrt{n} = 2.575*1.12[/tex]

[tex]\sqrt{n} = \frac{2.575*1.12}{0.1}[/tex]

[tex](\sqrt{n})^{2} = (\frac{2.575*1.12}{0.1})^{2}[/tex]

[tex]n = 831.7[/tex]

Rounding up

At least 832 teenargers must be interviewed.

Answer:

  B.  g(x)

Step-by-step explanation:

g(x) is a function of odd degree, so will tend toward negative infinity as an extreme value.

f(x) is an even-degree function with a positive leading coefficient. Its minimum value is -2.

g(x) has the smallest minimum value

Answer:

a) The third quartile Q₃ = 56.45

b) Variance [tex]\mathbf{ \sigma^2 =2633.31}[/tex]

Step-by-step explanation:

Given that :

[tex]Q_1[/tex]  =  30.8

Median [tex]Q_2[/tex] =  48.5

Mean  = 42

a) The mean is less than median; thus the expression showing the coefficient of skewness is given by the formula :

[tex]SK = \dfrac{Q_3+Q_1-2Q_2}{Q_3-Q_1}[/tex]

[tex]-0.38 = \dfrac{Q_3+30.8-2(48.5)}{Q_3-30.8}[/tex]

[tex]-0.38Q_3 + 11.704 = Q_3 +30.8 - 97[/tex]

[tex]1.38Q_3 = 77.904[/tex]

Divide both sides by 1.38

[tex]Q_3 = 56.45[/tex]

b) The objective here is to determine the approximate value of the variance;

Using the relation

[tex]SK_p = \dfrac{Mean- (3*Median-2 *Mean) }{\sigma}[/tex]

[tex]-0.38= \dfrac{42- (3 *48.5-2*42) }{\sigma}[/tex]

[tex]-0.38= \dfrac{(-19.5) }{\sigma}[/tex]

[tex]-0.38* \sigma = {(-19.5) }{}[/tex]

[tex]\sigma =\dfrac {(-19.5) }{-0.38 }[/tex]

[tex]\sigma =51.32[/tex]

Variance =  [tex]\sigma^2 =51.32^2[/tex]

[tex]\mathbf{ \sigma^2 =2633.31}[/tex]

Answer:

The other number is 25

See explanation below

Step-by-step explanation:

The question is incomplete. Since we were not given the area or the answer to the multiplication of the two numbers, I would show you how to multiply two 2-digit numbers using the area model.

Let's assume we want to find the area model of 27 and 25.

We would write the multiplicands(the two digit numbers) in expanded form as tens and ones.

So, 27 becomes 20 and 7

25 becomes 20 and 5.

Then draw a box that is 2 by 2 grid ( 2 rows and 2 columns)

Then multiply the 1st column by the 1st row, 2nd column by 2nd row. Afterwards sum the values obtained together.

For the question: 25×27

20×20, 20×5, 20×7, 5÷7

400, 100, 140, 35

Their sum = 400 + 100+ 140 +35

= 675

See attachment for diagram.

In this question only one of the numbers is given. The area of the two numbers wasn't given.

Assuming the area of the two numbers was given and one if the numbers was also given, we would apply area model of division.

Example: Area of the both numbers = 675, the other number given = 27. Find the other number.

The area model of solving division is gotten from finding the area of a rectangle.

Since Area of a rectangle = Length × Width

Then the the value of length would be greater than value of breadth.

675÷27 = 25

So break it down to 20 and 5. Hence You divide first by 20 in first column. Then divide the remainder (135) by 5 in second column.

See diagram for explanation

Answer:

2/1

Step-by-step explanation:

So you want to find a point where the line crosses a intersection near perfectly, point A (1,3) and then a second point, B (2,5)

and then you count up from point a, on the Y axis until you are even with the second point, that number is your RISE

it is 2

then you just count over to point B from that spot where you counted up. RUN TO IT

1

so it is 2/1 or just 2

((point (0,1) would have worked too))

Answer:

left, if looking from person's point of view

Step-by-step explanation:

Answer:

It would be A

Step-by-step explanation:

If you cut off the overlapping cubes, you get the image on A.

Answer:

x = pi/6

x = 11pi/6  

x = 5pi/6  

x =7pi/6

Step-by-step explanation:

2 sec^2 (x) + tan ^2 (x) -3 =0

We know tan^2(x) = sec^2 (x) -1

2 sec^2 (x) +sec^2(x) -1 -3 =0

Combine like terms

3 sec^2(x) -4 = 0

Add 4 to each side

3 sec^2 (x) = 4

Divide by 3

sec^2 (x) = 4/3

Take the square root of each side

sqrt(sec^2 (x)) = ±sqrt(4/3)

sec(x) = ±sqrt(4)/sqrt(3)

sec(x) = ±2 /sqrt(3)

Take the inverse sec on each side

sec^-1 sec(x) = sec^-1(±2 /sqrt(3))

x = pi/6 + 2 pi n    where n is an integer

x = 11pi/6 + 2 pi n  

x = 5pi/6 + 2 pi n  

x =7pi/6 + 2 pi n  

We only want the solutions between 0 and 2pi