The first step in determining the solution to the system of equations, y = –x2 – 4x – 3 and y = 2x + 5, algebraically is to set the two equations equal as –x2 – 4x – 3 = 2x + 5. What is the next step?

Set y = 0 in y = –x2 – 4x – 3.
Factor each side of the equation.
Use substitution to create a one-variable equation.
Combine like terms onto one side of the equation.

Answer:

Step-by-step explanation:

The table can be computed as:

Advertising Expenses ($ million)     Number of companies

25 up to 35                                                    4

35 up to 45                                                    19

45 up to 55                                                    27

55 up to 65                                                    16

65 up to 75                                                     9

TOTAL                                                            75

Let's find the probabilities first:

[tex]P(25 - 35) = P \Big(\dfrac{25-50.93}{10.80}<z< \dfrac{35-50.93}{10.80}\Big) \\ \\ =P \Big(\dfrac{-25.93}{10.80}<z< \dfrac{-15.93}{10.80}\Big) \\ \\ =P(-2.4009<z<-1.475) \\ \\ =(0.0694 -0.0082) \\ \\ =0.0612[/tex]

For 35 up to 45

[tex]P(35 - 45) = P \Big(\dfrac{35-50.93}{10.80}<z< \dfrac{45-50.93}{10.80}\Big)=P \Big(\dfrac{-15.93}{10.80}<z< \dfrac{-5.93}{10.80}\Big) \\ \\ =P(-1.475<z<-0.5491) \\ \\ =(0.2912 -0.0694) \\ \\ =0.2218[/tex]

For 45 up to 55

[tex]P(45 - 55) = P \Big(\dfrac{45-50.93}{10.80}<z< \dfrac{55-50.93}{10.80}\Big)=P \Big(\dfrac{-5.93}{10.80}<z< \dfrac{4.07}{10.80}\Big) \\ \\ =P(-0.5491<z<0.3769) \\ \\ =(0.6480 -0.2912) \\ \\ =0.3568[/tex]

For 55 up to 65

[tex]P(55 - 65) = P \Big(\dfrac{55-50.93}{10.80}<z< \dfrac{65-50.93}{10.80}\Big)=P \Big(\dfrac{4.07}{10.80}<z< \dfrac{14.07}{10.80}\Big) \\ \\=P(0.3768<z<1.3028) \\ \\ =(0.9032-0.6480) \\ \\ =0.2552[/tex]

For 65 up to 75

[tex]P(65 - 75) = P \Big(\dfrac{65-50.93}{10.80}<z< \dfrac{75-50.93}{10.80}\Big)=P \Big(\dfrac{14.07}{10.80}<z< \dfrac{24.07}{10.80}\Big) \\ \\ =P(1.3028<z<2.2287) \\ \\=(0.9871-0.9032) \\ \\ =0.0839[/tex]

Chi-Square Table can be computed as follows:

Expense   No of   Probabilities(P)  Expe                [tex](O-E)^2[/tex]   [tex]\dfrac{(O-E)^2}{E}[/tex]

             compa                                 cted E (n*p)

             nies (O)  

25-35           4      0.0612    75*0.0612 = 4.59        0.3481       0.0758

35-45           19     0.2218   75*0.2218 = 16.635     5.5932       0.3362

45-55           27     0.3568   75*0.3568 = 26.76     0.0576      0.021

55-65           16      0.2552   75*0.2552 = 19.14      9.8596      0.5151

65-75           9      0.0839     75*0.0839 = 6.2925   7.331         1.1650

                                                                                           [tex]\sum \dfrac{(O-E)^2}{E}= 2.0492[/tex]                                                                                                      

Using the Chi-square formula:

[tex]X^2 = \dfrac{(O-E)^2}{E} \\ \\ Chi-square \ X^2 = 2.0942[/tex]

Null hypothesis:

[tex]H_o: \text{The population of advertising expenses follows a normal distribution}[/tex]

Alternative hypothesis:  

[tex]H_a: \text{The population of advertising expenses does not follows a normal distribution}[/tex]

Assume that:

[tex]\alpha = 0.02[/tex]

degree of freedom:

= n-1

= 5 -1

= 4

Critical value from [tex]X^2 = 11.667[/tex]

Decision rule: To reject [tex]H_o \ if \ X^2[/tex]  test statistics is greater than [tex]X^2[/tex] tabulated.

Conclusion: Since [tex]X^2 = 2.0942[/tex] is less than critical value 11.667. Then we fail to reject [tex]H_o[/tex]

Answer: 63 copies were sold yesterday.

Step-by-step explanation: To find how many copies were sold yesterday, simply multiply 81 by 7 which is 567. Then, divide 567 by 9 which is 63.

-4× = 16 answer: -4

Step-by-step explanation:

-4 × -4 = 16

Answer: 1/2x

Step-by-step explanation:

Answer:

You are right; It is Figure B

Step-by-step explanation:

9514 1404 393

Explanation:

Statement .... Reason

( ) .... Given (repeat of the given statements)

ΔACB ≅ ΔDCE .... SAS postulate

BA ≅ ED .... corresponding parts of congruent triangles are congruent

Answer:

1 and -8

Step-by-step explanation:

I just substituted them until I found the correct one.

Hope this helps ^-^

Answer:

Step-by-step explanation:

Volume of a cone is given by the formula,

V = [tex]\frac{1}{3}\pi r^{2}h[/tex]

Here, r = Radius of the circular base of the cone

h = Height

By substituting values from the question,

V = [tex]\frac{1}{3}\times \pi (\frac{6}{2})^2(3)[/tex]

V = 9π

V = 28.27 m³ [Nearest hundred]

If we have to round the answer to the nearest tenth, answer will be,

Volume = 28.3 m³

If we have have to round the answer to the whole number then the answer will be,

Volume = 28 m³  

Answer:

105 rabbits

Step-by-step explanation:

Multiple 5 percent by six days

5%x6=30%

150 rabbits --- 100%

x ----- 30%

100x=150x30

100x=4500 : 100

x=45

150-45=105

Answer:

880

Step-by-step explanation:

I've taken 5/105 divided and gotten 20.I have taken 20 * 6 which is the decrease so that you can get after six days how many rabbits were decreased and 150 * 6 that you can get how many rabbits are there in 6 days.then I took 900 - 120 i go 880 rabbits hope that helps.

Answer:

(x+6)

Step-by-step explanation:

because you have ( x+6) on bottom of the first equation and on the top on the second equation

Answer:

I believe the answer is D coorrect me if im wrong

Step-by-step explanation:

if im right brainliest?

or 5 stars and heart

Answer:

y=5x

Step-by-step explanation:

The slope of the line is the same as the original equation, with the 3 just shifting the line down 3 spots on the y axis.

Answer:

A will be the answer hope this will help u

Answer:

the correct option is A. (-5,-7)

like (5,-7) I. e (+,-) lies in the 3rd quadrant and the opposite of 3rd quadrant vertically is the 2nd quadrant.

so, the answer should come as (-,-) according to the 2nd quadrant.

so, answer will be (-5,-7)

I hope it's correct.

Answer:

The 98% confidence interval for the population proportion of disks which are defective is (0.082, 0.118).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

Suppose a sample of 1536 floppy disks is drawn. Of these disks, 1383 were not defective.

1536 - 1383 = 153

This means that [tex]n = 1536, \pi = \frac{153}{1536} = 0.1[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1 - 2.327\sqrt{\frac{0.1*0.9}{1536}} = 0.082[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1 + 2.327\sqrt{\frac{0.1*0.9}{1536}} = 0.118[/tex]

The 98% confidence interval for the population proportion of disks which are defective is (0.082, 0.118).

Answer:

C. 5

Step-by-step explanation:

Use the Distance Formula.

Substitute the values of x1 , y1 , x2 , and y2 .

|AB|² =|(1--2)²+(10-6)²|

|AB|² = |9+16|

|AB| = √ 25

|AB| =5

Answer:

19 degrees

Step-by-step explanation:

Sum of 2 angles is complementary,

x + 71 = 90

x = 90 - 71

x = 19 degrees

Answer:

x = 7.31 cm

Step-by-step explanation:

cos 70° = 3.8/AB

0.3420 = 3.8/AB

AB = 11.11 cm

x = 11.11 - 3.8 = 7.31 cm

The value of x which is the radius of circle A is 7.31 cm

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

AB = AC, hence ∠B = ∠C = 70°

∠A + ∠B + ∠C = 180° (angles in a triangle)

∠A + 70 + 70 = 180

∠A = 40°

BC = 3.8 + 3.8 = 7.6

Using sine rule:

BC/sinA = AB / sinB

7.6/sin(40) = AB/sin(70)

AB = 11.11 cm

x = 11.11 - 3.8 = 7.31 cm

The value of x which is the radius of circle A is 7.31 cm

Find out more on equation at: https://brainly.com/question/2972832

Step-by-step explanation:

Im donating points thank you

Answer:

do you have a graph? we can't do it unless you have one.

Answer:

t = 45

Step-by-step explanation:

[tex]\frac{t}{15} = \frac{3}{1}[/tex]

t × 1 = 15 × 3

t = 45

Answer:

w = 3.39 in

l = 13.56 in

Step-by-step explanation:

46 = w(4w) = 4w²

w² = 11.5

w = 3.39 in

l = 13.56 in

Answer:

[tex] \frac{45π}{2} \: units^{2} \: ≈ \: \boxed{70.7 \: units²} [/tex]

______________________

The correct option is 70.7

Step-by-step explanation:

Since the green and red make a semicircle, the total measure must be 180°.

Since the two green sectors are both 40°.

The red must add up with the green sectors to total 180°.

This means that:

red sector + 80° = 180°.

–80° –80.

red sector = 100°.

To find the area of a sector, we must first understand the area of the circle itself which is πr², where r is the radius.

Since a full circle is 360°.

(360° / 360°)( πr² ) will be the area.

Or in radians: (2π rad / 2π rad)( πr² ).

From here, we can create the formula:

Area of a sector = ( n° / 360° ) ( πr² ). Where n is the measure or the sector in degrees, and r is the radius.

You may also know that the diameter is twice the measure of the radius.

This means that if we are given a diameter of 18 units from the problem, the radius will be 18/2 or 9 units.

Lastly, all we have to do is substitute all this information to find the area of sector.

Area of the red sector = ( n° / 360° ) ( πr² ).

Area of the red sector =

( (100°) / 360° ) ( π(9)² ).

Area of the red sector = ( 5 / 18 ) ( 81π )

Area of the red sector = ( (5)(81π) / 18 )

Area of the red sector = ( (405π) / 18 )

Area of the red sector = ( 45π / 2 ) units²

Area of the red sector =

(141.371669412.. units²) / 2

Area of the red sector =

70.6858347058.. units²

Area of the red sector ≈

70.7 units²

The graphs intersect at the points (3, 13) and (-2, -7).

Given the following equations:

y₁ = x² + 3x - 5  (quadratic equation)

y₂ = 4x + 1 (linear equation)

To find the intersection point(s) of  the two graphs, we need to solve their equations simultaneously. By so doing, we'll set the equations equal to each other:

y₁ = y₂

x² + 3x - 5 = 4x + 1

collect the like terms

x² - x - 6 = 0

Now we'll factor the quadratic expression:

(x - 3)(x + 2) = 0

x - 3 = 0 or x + 2 = 0

x = 3 or x = -2

Now we have the points of intersection on the x-axis.

To get the corresponding  values on the y-axis, we'll plug each value of x into either of the original equations.

Let's use the first equation:

y₁ = x² + 3x - 5

When x = 3:

y₁ = 3² + 3(3) - 5 = 13

When x = -2:

y₂ = 4x + 1 = 4(-2) + 1 = -7

So the first intersection point is (3, 13) and the second intersection point is (-2, -7).

Therefore, the graphs intersect at the points (3, 13) and (-2, -7).

Learn more about intersection here:

https://brainly.com/question/29185601

#SPJ1

Answer:

112

Step-by-step explanation:

25 = 1/4 of 100. so u gotta do 4 * 28

Answer:7

Step-by-step explanation:

Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Length of remnant fabric = 9.7m

Number of 0.85m length needed for patio = 12

Total length needed = (0.85 * 12) = 10.2m

The length of fabric needed is more than the length of remnant fabric found ;

10.2 m - 9.7m = 0.5m

Hence, Alex will need 0.5m more fabric

Answer

20384

Step-by-step explanation:

Answer:

90.35

Step-by-step explanation:

its on envisions

8-2 quiz