What point lies on the line described by the equation below? Y+3=2 (x-1

Answer:

There are 2 * 32 = 64 possible ways for choosing three course meal.

Step-by-step explanation:

1-If we choose an appetizer, main course and a soup then there are 32 ways to choose this three course meal. 4 * 2 * 4 = 32 ways. There will be an appetizer, main course and a soup in the meal.

2-If we choose a soup, main course and a dessert then there are 32 ways to choose this three course meal. 4 * 2 * 4 = 32 ways. There will be a soup, main course and a dessert in the meal.

There are 2 possible ways to choose either an appetizer or dessert in a 3 course meal. There will be 64 ways in total for the three course meal.

Answer:

[tex]\mathrm{B.}[/tex] All real numbers except x = 2, x = 5

Step-by-step explanation:

If the denominator is equal to 0 then the function would be undefined.

Set the denominator equal to 0.

x² - 7x + 10 = 0

Factor the left side of the equation.

(x - 5)(x - 2) = 0

Set the factors equal to 0.

x - 5 = 0

x = 5

x - 2 = 0

x = 2

The domain is all real numbers except x = 2 and x = 5.

Answer:

x1= -4, x2 = 7

Step-by-step explanation:

Move expression to the left-hand side:

1/4x-3/4-7/x=0

Write all the numerators above a common denominator:

x^2 - 3x - 28 /4x =0

When the quotient of expressions equal 0, the numerator has to be 0

x^2 + 4x - 7x - 28 = 0

x(x+4) - 7(x+4) =0

(x+4) × (x-7) =0

Separate into possible cases:

x+4=0

x-7=0

Answer: -9

Step-by-step explanation:

Answer:

5,2

Step-by-step explanation: (-7+12=5,-6=8=2) And I Got It Correct On Khan Academy :)

Hope this helps you!!

The coordinate of Q under the translation (x,y)→(x+12,y+8) will be located at Q'(5, 2)

Translation of image is a mathematical term used to move an object through a distance.

Given the coordinate point Q(-7, 6), if this coordinate is under the translation (x,y)→(x+12,y+8), this means we are to shift the x coordinate of Q to the right by 12units and the y-coordinates of Q up by 8 units to get the new location at Q'. Hence:

Q' = (-7 + 12, -6 + 8)

Q' = (5, 2)

This shows that the coordinate of Q under the translation (x,y)→(x+12,y+8) will be located at Q'(5, 2)

Learn more about translation here: https://brainly.com/question/10704056

Answer:

Step-by-step explanation:

Total inches grown last year by matthew = 2.7inches

Total inches grown this year by Matthew = 4.4 inches

Total inches grown by Matthew over the last two years combined will be the sum of heights of matthew for both the previous year and the current year.

Total inches grown = 2.7 inches + 4.4 inches

Total inches grown over the last two years = 7.1 inches

Answer:

[tex]\large \boxed{\sf \ \ x=0, \ \ y=-5 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We have two equations:

(1) -2x - 4y = 20

(2) -3x + 5y = -25

5*(1)+4*(2) gives

   -10x - 20y -12x + 20y = 100 - 100 = 0

   -22x = 0

   x = 0

I replace in (1)

   -4y = 20

   y = -20/4 = -5

There is one solution x = 0, y = -5

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The two equations are

-2x-4y=20

-3x+5y=-25

multiply equation 1 by 5 and equation 2 by 4

-10x-20y=100

-12x+20y=-100

-22x=0

x=0

Substitute value in either equation

y=-5

So,option 1 is correct only one solution

Complete Question

A committee has six members. There are three members that currently serve as the​ board's chairman comma vice chairman comma and treasurer . Each member is equally likely to serve in any of the positions. Three members are randomly selected and assigned to be the new chairman comma vice chairman comma and treasurer . What is the probability of randomly selecting the three members who currently hold the positions of chairman comma vice chairman comma and treasurer and reassigning them to their current​ positions?

The probability is ?

Answer:

The probability is [tex]P(3 ) = \frac{ 1 }{20 }[/tex]

Step-by-step explanation:

From the question we are told that

       The total number of members is  n = 6  

       The  number of member to be selected is  r =  3  

Generally the number of ways of selecting 3 members from 6  is mathematically evaluated as

          [tex]\left n } \atop {}} \right. C _r = \frac{n! }{(n-r ) ! r !}[/tex]

=>       [tex]\left 6 } \atop {}} \right. C _ 3 = \frac{6 ! }{(6-3) ! 3 !}[/tex]

=>        [tex]\left n } \atop {}} \right. C _r = \frac{6* 5* 4 * 3! }{3 ! 3*2 * 1}[/tex]

=>       [tex]\left n } \atop {}} \right. C _r = \frac{6* 5* 4 }{3 *2 * 1}[/tex]

=>        [tex]\left n } \atop {}} \right. C _r =20[/tex]

Now the number of ways of selecting the 3 members who currently hold the position is  n  = 1

  So the probability is mathematically represented as

                 [tex]p(k ) = \frac{ n }{\left n } \atop {}} \right. C _r }[/tex]

substituting values

                  [tex]P(3 ) = \frac{ 1 }{20 }[/tex]

Answer:

79.95, 82.62

Step-by-step explanation:

using excel to find a 95% confidence interval for the mean bounce height of the golf ball

Heights given are :

81.4

80.8

84.4

85.6

82.9

76.0

80.0

83.2

80.8

79.6

82.9

83.4

82.2

86.0

76.2

84.8

82.0

76.3

77.0

75.4

82.0

79.8

80.4

86.9

82.1

The statistical out put of the problem after solving with excel is attached below

therefore the 95% confidence interval from the attached solution will be ( 79.95, 82.62 )

Answer: (79.95, 82.61)

Step-by-step explanation:

Use Excel to calculate the 95% confidence interval, where α=0.05 and n=25.

1. Open Excel and enter the given data in column A. Find the sample mean, x¯, using the AVERAGE function and the sample standard deviation, s, using the STDEV.S function. Thus, the sample mean, rounded to two decimal places, is 81.28 and the sample standard deviation, rounded to two decimal places, is 3.23.

2. Click on any empty cell, enter =CONFIDENCE.T(0.05,3.23,25), and press ENTER.

3. The margin of error, rounded to two decimal places, is 1.33. The confidence interval for the population mean has a lower limit of 81.28−1.33=79.95 and an upper limit of 81.28+1.33=82.61.

Thus, the 95% confidence interval for the mean bounce height of the golf balls is (79.95, 82.61).

Answer:

Step-by-step explanation:

Hello!

For this particular organism population the growth rate is so that is doubled every 20 years. Using the starting population of 9 billion individuals by year 2000 you have to calculate the expected population values every 20 years.

All you have to do is multiply the original population by 2 to obtain the next value.

Year 2000:

Population: 9*10⁹ or 9 000 000 000 x 2= 18 000 000 000

To express 18 billion in  scientific notation you have to add a "comma" after the first digit and then count the number of digits behind it:

1, 8 000 000 000 there are 10 digits behind the first digit. This notation  summarizes the number in base 10 exponents so 18 billion in scientific notation is:

1.8 * ten "exponent the number of digits behind the comma"

1,8*10¹⁰So the population for year 2020 will be 1,8*10¹⁰

Next for year 2040 you have to multiply the population of year 2020 by 2

1,8*10¹⁰ x 2= 3,6*10¹⁰

And so on:

2060: 3,6*10¹⁰ x 2)= 7.2*10¹⁰

2080: 7.2*10¹⁰ x2= 1.44*10¹¹

2100: 1.44*10¹¹ x2= 2.88*10¹¹

2120: 2.88*10¹¹x2= 5.76*10¹¹

2140: 5.76*10¹¹x2= 1.152*10¹²

2160: 1.152*10¹²x2= 2.304*10¹²

2180: 2.304*10¹²x2= 4.608*10¹²

2200: 4.608*10¹² x2= 9.216*10¹²

2220: 9.216*10¹²x2= 1.8432*10¹³

2240: 1.8432*10¹³x2= 3.6864*10¹³

2260: 3.6864*10¹³x2= 7.3728*10¹³

2280: 7.3728*10¹³x2= 1.47456*10¹⁴

2300: 1.47456*10¹⁴x2= 2.94912*10¹⁴

2320: 2.94912*10¹⁴x2= 5.89824*10¹⁴

2340: 5.89824*10¹⁴x2= 1.179648*10¹⁵

2360: 1.179648*10¹⁵x2= 2.359296*10¹⁵

2380: 2.359296*10¹⁵x2= 4.718592*10¹⁵

2400: 4.718592*10¹⁵x2= 9.437184*10¹⁵

So for year 2400 the expected population will be 9.437184*10¹⁵, writen in common notation that is:

9 437 184 000 000 000 individuals

I hope this helps!

Answer:

B. 4

Step-by-step explanation:

Let the side of the square= a

Then the area of the square= a²

Given:

Then:

Considering the value of the area, 12 units

Correct choice is B. 4

Answer:

a[tex]\geq[/tex]-3

Step-by-step explanation:

Answer:

-3  ≤  a

Step-by-step explanation:

6≥ -6(a+2)

Divide each side by -6, remembering to flip the inequality

6/-6 ≤ -6/-6(a+2)

-1 ≤ (a+2)

Subtract 2 from each side

-1 -2  ≤  a+2-2

-3  ≤  a

Answer:

A.

Step-by-step explanation:

Hello,

g(x-4)=f(x) so the graph of g is the graph of f shifted 4 units to the left.

For any x, the point (x-4, g(x-4)) is 4 units to the left of the point (x,f(x)).

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

A

Step-by-step explanation:

:) i just took the test and it was right

Answer: (84.876, 87.124)

Step-by-step explanation:

Confidence interval for population mean if population standard deviation is unknown:

[tex]\overline{x}\pm t_{\alpha/2}(\dfrac{s}{\sqrt{n}})[/tex]

, where n= sample size

s= sample standard deviation

[tex]\overline{x}[/tex] = sample mean

[tex]\alpha=[/tex] significance level

[tex]t_{\alpha/2}[/tex] = critical-t value

Given:  n= 64

Degree of freedom = n-1 = 63

s= 4.5

[tex]\overline{x}[/tex] = 86

[tex]\alpha=[/tex] 0.05

[tex]t_{\alpha/2}[/tex] = 1.9983

Now, the required 95% confidence interval would be:

[tex]86\pm (1.9983)(\dfrac{4.5}{\sqrt{64}})\\\\=86\pm (1.9983)(\dfrac{4.5}{8})\\\\=86\pm (1.9983)(0.5625)\\\\\approx86\pm 1.1240\\\\ =(86-1.1240,\ 86+1.1240)\\\\=(84.876,\ 87.124)[/tex]

The 95% confidence interval for the population mean μ is between: (84.876, 87.124)

Answer:

The pie chart representing for this question is presented in the attached image to this solution.

Step-by-step explanation:

Complete Question

Draw a pie chart for the percent of the money spent on various types of books by a library in a year.​

Type of book | %

Fiction | 20%

Classics | 15%

Sports | 10%

Biography | 12.5%

Magazines | 22.5%

Others | 20%

Solution

A pie chart is a graphical representation of a set of numerical data which comes in a circular shape divided into slices, with the size of each slice corresponding to the proportion of the numerical data it represents.

Because it is a circle, the total angles in a pie chart is 360°.

The angles are divided into slices with the size of each slice corresponding to how large the data it represents is.

So, we first convert the data given into degrees.

Since the data is given in percentage, for each of the groups, the conversion from percentage will be

Angle = (Proportion) × 360°

Type of book | % | Angle

Fiction | 20% | 72°

Classics | 15% | 54°

Sports | 10% | 36°

Biography | 12.5% | 45°

Magazines | 22.5% | 81°

Others | 20% | 72°

The pie chart representing this data is presented in the attached image to this solution.

Hope this Helps!!!

Answer:

  64.8 and 75.2

Step-by-step explanation:

A suitable probability calculator can show you the middle 40% is between about 64.8 and 75.2.

Answer:

A. 70 dimes, 30 quarters

Step-by-step explanation:

Only options A and B create a total of 100 coins. It cannot be option B because 80 quarters by itself, is already over $14.50.

Answer:

8(7 + 4) = 88

Step-by-step explanation:

56:

1 x 56

2 x 28

4 x 14

7 x 8

32:

1 x 32

2 x 16

4 x 8

Answer:

8(7+4)

Step-by-step explanation:

Use the binomial theorem:

[tex](1+1)^{16}=\displaystyle\sum_{k=0}^{16}\binom{16}k1^{16-k}1^k[/tex]

So

[tex]\dbinom{16}0+\dbinom{16}1+\cdots+\dbinom{16}{16}=\boxed{2^{16}}[/tex]

More generally,

[tex]\displaystyle\sum_{k=0}^n\binom nk=2^n[/tex]

Answer:

answer is

B) 36,72,80

Step-by-step explanation:

because is the right angle it is exactly 90°

Answer:

solution

given a=1_9k and b=j+k

Now,ab=(1_9k)(j+k)

=1((j+k)-9k(j+k)

=j+k_9jk-9k^2

=k_9k^2+j_9jk

=k((1_9k)+j(1_9k)

=(1_9k)(k+k)

Answer:

Step-by-step explanation:

when h(t)=0

-4.9 t²+19.6t=0

4.9t(-t+4)=0

either t=0 or t=4

so domain is 0≤t≤4

for range

h(t)=-4.9t²+19.6t

=-4.9(t²-4t+4-4)

=-4.9(t-2)²+19.6

so range is 0≤h≤19.6

Domain = 0<t<4, make sure to use less than or equal to signs not just less than signs.

Range = 0<h<19.6, again, use less than or equal to signs.

Answer:

0.0499

Step-by-step explanation:

The p-value can be calculated using technology. The p-value is computed by using F distribution right tailed excel function. The excel function "F.DIST.RT(4.76,3,6)" gives desired p-value which is 0.0499.

The p-value shows that the for 5% level of significance the null hypothesis can be rejected.

Answer:

a = 6, b = 7, c = 8, d = 7 and e = 6

Step-by-step explanation:

Let's remember that the complete revolution of the wheel is 360 degrees, and the distance traveled by a complete revolution is the length of the circumference: 2*pi*radius.

The inicial height of the point is 6 ft, and the radius of the wheel is 1 ft.

When the distance traveled is 0, the wheel turned 0 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.

So the height will be a = 6 + 0 = 6 ft

When the distance traveled is pi/2, the wheel turned 90 degrees, and the point will be half the complete height of the wheel, which is 2 feet.

So the height will be b = 6 + 1 = 7 ft

When the distance traveled is pi, the wheel turned 180 degrees, and the point will be at the top of the wheel, which is 2 feet higher than the lower point of the wheel.

So the height will be c = 6 + 2= 8 ft

When the distance traveled is 3pi/2, the wheel turned 270 degrees, and the point will be half the complete height of the wheel, which is 2 feet.

So the height will be d = 6 + 1 = 7 ft

When the distance traveled is 2pi, the wheel turned 360 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.

So the height will be e = 6 + 0 = 6 ft

So the answers are:

a = 6, b = 7, c = 8, d = 7 and e = 6

Answer:

6, 7, 8, 7, 6

Step-by-step explanation:

Answer:

The answer should be B: 5n+300=1,500.

Step-by-step explanation:

The number of people to attend is going to vary and 300 is a set variable, so it won't change of be affected. Since the team doesn't know how many people will be able to attend in order to reach their goal, n is going to take the place for the amount of people.

If you were to solve this, the answer would be:

5n+300=1,500

5n=1,500-300

5n=1,200

n=240

So 240 people can attend the dance.

Answer:5n-300=1,500

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

7 supersricpt 8

Problem 3

----------

Work Shown:

Use either the FOIL method, distributive property, or the box method to get the following

(x-2)*(x-5) = x^2 - 5x - 2x + 10 = x^2 - 7x + 10

==========================================

Problem 4

----------

Work Shown:

Same idea as problem 3 above

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

Answer:

3. y = x² - 7x + 10

4. y = x² - x - 6

Step-by-step explanation:

Answer:  B) 10 three-point questions and 14 five-point questions

Step-by-step explanation:

x represents three-point questions

y represents five-point questions

3x + 5y = 100  →  1(3x + 5y = 100)  =  3x + 5y = 100

 x  +  y  = 24   → -3(x  +  y  = 24)   = -3x  -3y  = -72

                                                                  2y = 28

                                                                    y = 14  (five-point questions)

x +  y = 24

x + 14 = 24

     x = 10  (three-point questions)

Answer:

x = 28, y = 23

Step-by-step explanation:

5y - 4 and 3y are alternate exterior angles and are supplementary, thus

5y - 4 + 3y = 180

8y - 4 = 180 ( add 4 to both sides )

8y = 184 ( divide both sides by 8 )

y = 23

Thus

3y = 3 × 23 = 69

2x + 13 and 3y are corresponding angles and congruent, thus

2x + 13 = 69 ( subtract 13 from both sides )

2x = 56 ( divide both sides by 2 )

x = 28