a line has an x-intercept of (4,0) and a y-intercept of (0,12).Find the slope of the line

Answer: D. [tex]y+4=(x+2)[/tex]

Step-by-step explanation: Once you subtract [tex]4[/tex] from both sides, in order to solve for y (as the equation needs to be in the slope-intercept form, otherwise known as [tex]y=mx+b[/tex]), you end up with [tex]y=x-2[/tex], which is the right answer. It is the correct answer because the y-intecept shown in the equation matches what is on the graph, in addition to the fact that the slope is just [tex]x[/tex].

Answer:

The random variable (number of toppings ordered on a large pizza) has a mean of 1.14 and a standard deviation of 1.04.

Step-by-step explanation:

The question is incomplete:

The probability distribution is:

x   P(x)

0   0.30

1    0.40

2   0.20

3   0.06

4   0.04

The mean can be calculated as:

[tex]M=\sum p_iX_i=0.3\cdot 0+0.4\cdot 1+0.2\cdot 2+0.06\cdot 3+0.04\cdot 4\\\\M=0+0.4+0.4+0.18+0.16\\\\M=1.14[/tex]

(pi is the probability of each class, Xi is the number of topping in each class)

The standard deviation is calculated as:

[tex]s=\sqrt{\sum p_i(X_i-M)^2}\\\\s=\sqrt{0.3(0-1.14)^2+0.4(1-1.14)^2+0.2(2-1.14)^2+0.06(3-1.14)^2+0.04(4-1.14)^2}\\\\s=\sqrt{0.3(-1.14)^2+0.4(-0.14)^2+0.2(0.86)^2+0.06(1.86)^2+0.04(2.86)^2}\\\\ s=\sqrt{0.3(1.2996)+0.4(0.0196)+0.2(0.7396)+0.06(3.4596)+0.04(8.1796)}\\\\s=\sqrt{0.3899+0.0078+0.1479+0.2076+0.3272}\\\\ s=\sqrt{ 1.0804 }\\\\s\approx 1.04[/tex]

Answer:

mean: 1.14; standard deviation: 1.04

Step-by-step explanation:

Answer:

D. 120

Step-by-step explanation:

Array formula: A (n, p) = n! / (n -p)!

At where:

 n = Total number of elements in the set.

p = Quantity of elements per arrangement

A (5.5) = 5! / (5-5)! = (5x4x3x2x1) / 0!

By definition: 0! = 1

Then: 120/1 = 120

Answer:

r = -10*cos(t)

Step-by-step explanation:

To write the rectangular equation in polar form we need to replace x and y by:

[tex]x=r*cos(t)\\y=r*sin(t)[/tex]

Replacing on the original equation, we get:

[tex](x+5)^2+y^2=25\\x^2+10x+25+y^2=25\\(r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25[/tex]

Using the identity [tex]sin^2(t)+cos^2(t)=1[/tex] and solving for r, we get that the polar form of the equation is:

[tex](r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25\\r^2cos^2(t)+10rcos(t)+r^2sin^2(t)=0\\r^2cos^2(t)+r^2sin^2(t)=-10rcos(t)\\r^2(cos^2(t)+sin^2(t))=-10rcos(t)\\r^2=-10rcos(t)\\\\r=-10cos(t)[/tex]

Answer:

A: x= -1 or x=3

B: Since the quadratic equation has two real solutions, the graph of the quadratic equation intercepts the x axis at (-1,0) and (3,0)

Step-by-step explanation:

x^2 -2x -3 =0

Factor

(x-3 )(x+1) =0

Using the zero product property

x-3 =0   x+1 =0

x=3  x=-1

The zeros are

(3,0) (-1,0)

It intersects the x axis at (3,0) (-1,0)

Answer:

49π m² or 153.94 m²

Step-by-step explanation:

Area of a circle: A = πr²

We are given r as 7, so simply plug it in

A = π(7)^2

A = 49π m²

Answer:

4 : 3

Step-by-step explanation:

16 : 12 can be simplified by 4 to get 4 : 3

Answer:

[tex]4:3[/tex]

Step-by-step explanation:

[tex]16 : 12[/tex]

The common highest factor of the ratio is 4.

Simplify the ratio.

[tex]16 \div 4:12 \div 4[/tex]

[tex]4:3[/tex]

Answer:5. 291503

Step-by-step explanation:

√28

2√7

5. 291503

Answer:

AT least 14 classrooms to hold the total number of students

Step-by-step explanation:

Since  we don't know the numer of girls in the school, let's call it "x".

What we know is that the number of girls plus the number of boys gives the total number of students. This is:

x + 129 = Total number of students

Now, since 5/8 of the total number of students are girls, and understanding that 5/8 = 0.625 in decimal form, then we write the equation that states:

"5/8 of the school's population are girls" as:

0.625 (x + 129) = x

then we solve for "x":

0.625 x + 0.625 * 129 = x

0.625 * 129 = x - 0.625 x

80.625 = x (1 - 0.625)

80.625 = 0.375 x

x = 80.625/0.375

x = 215

So now we know that the total number of students is: 215 + 129 = 344

and if each classroom can hold 25 students, the number of classroom needed for 344 students is:

344/25 = 13.76

so at least 14 classrooms to hold all those students

◇Given :-

The denominator of a fraction is increased by a number and numerator will be doubled

To find

We have to find the required number or fraction

[tex]\underline{\bigstar{\sf\ \ Solution:-}}[/tex]

Now let us consided as the number be a

Then

The given fraction is 5/9

[tex]:\implies\sf \dfrac{5\times 2}{9+a}= 1\\ \\ \\ :\implies\sf \dfrac{10}{9+a}=1\\ \\ \\ :\implies\sf 10= 1(9+a)\\ \\ \\ :\implies\sf 10-9=a\\ \\ \\ :\implies\sf 1=a [/tex]

Answer:

B, C and D

Step-by-step explanation:

Given:

Statement: "Every integer has an additive inverse"

To find: statement that is equivalent to the given statement

Solution:

For any integer x, if [tex]x+y=0[/tex] then y is the additive inverse of x.

Here, 0 is the additive identity.

Statements ''All integers have additive inverses '', '' If x is an integer, then x has an additive inverse'' and  ''Given an integer x, there exists a y such that y is the additive inverse of x'' are equivalent to the given statement "Every integer has an additive inverse".

Answer:

[tex]-15.11[/tex]

Step-by-step explanation:

[tex]-12.48-(-2.99)-5.62=\\-12.48+2.99-5.62=\\-9.49-5.62=\\-15.11[/tex]

Answer:

-15.11

Step-by-step explanation:

-12.48+2.99-5.62=

-9.49 - 5.62= - (9.49+5.62)=-15.11

Answer:

False

Step-by-step explanation:

from *millermoldwarp*

"Events are called dependent when the probability of an event depends on the occurrence of another. When event A depends on event B, the probability that A occurs, given that B has occurred, is different from the probability that A occurs only ."

hopes this helps

Answer:false

Step-by-step explanation:

Answer:

22.11 miles per gallon

Step-by-step explanation:

1 km = 0.621371 miles

1 litre = 0. 264172 gallon

Given

Mileage of car =  9.4 Milometers per liter of gasoline

Mileage of car = 9.4 Km/ litres

now we will use 0.621371 miles for Km and 0. 264172 gallon for litres

Mileage of car = 9.4 * 0.621371 miles/ 0. 264172 gallon

Mileage of car = 9.4 * 2.3521 miles/ gallon

Mileage of car = 22.11  miles/ gallon

Thus, 9.4 Km/litres is same as 22.11 miles per gallon.

Answer:1260

Step-by-step explanation:

Kissing has 7 letters, and there are 2 paris of the same letter.

[tex]\frac{7!}{2!2!}[/tex] = [tex]\frac{7*6*5*4*3*2*1}{4}[/tex]= 1260

Complete question is;

A utility company offers a lifeline rate to any household whose electricity usage falls below 240 kWh during a particular month. Let A denote the event that a randomly selected household in a certain community does not exceed the lifeline usage during January, and let B be the analogous event for the month of July (A and B refer to the same household). Suppose P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8. Compute the following.

a. P(A ∩ B).

b. The probability that the lifeline usage amount is exceeded in exactly one of the two months.

Answer:

A) 0.4

B) 0.4

Step-by-step explanation:

We are given;

P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8

A) To solve this question, we will use the the general probability addition rule for the union of two events which is;

P(A∪B) = P(A) + P(B) − P(A∩B)

Making P(A∩B) the subject of the equation, we have;

P(A∩B) = P(A) + P(B) − P(A∪B)

Thus, plugging in the relevant values, we have;

P(A∩B) = 0.7 + 0.5 - 0.8

P(A∩B) = 0.4

B)The probability that the lifeline usage amount is exceeded in exactly one of the two months can be described in terms of A and B as:

P(A but not B) + P(B but not A) = P(A∩B') + P(B∩A')

where;

A' is compliment of set A

B' is compliment of set B

Now,

P(A∩B') = 0.7 − 0.4 = 0.3

P(B∩A') = 0.5 − 0.4 = 0.1

Thus;

P(A but not B) + P(B but not A) = 0.1 + 0.3 = 0.4

Answer:

The recurrence relation for aₙ is  aₙ = 2aₙ - 1 + 2aₙ -2 ; is n≥ 3 with the initial conditions as a₁ =3; a₂ = 8

Step-by-step explanation:

Solution

Recurrence relation for n - digit ternary sequence with no occurrence of consecutive 0's in them.

Ternary sequence is sequence with each of digits either 0, 1 or 2.

Now

Let aₙ = denote the number of n - digit ternary sequence with no occurrence of consecutive 0's in them.

Let us first find few initial values of aₙ

For n = 1

a₁ represent the number of 1- digit ternary sequence with no occurrence of consecutive 0's in them.  

This 1-digit sequence can be either 0 or 1 or 2.

Thus,

a₁ = 3

For n =2

a₂ represent the number of 2- digit ternary sequence with no occurrence of consecutive 0's in them.

This 2-digit sequence can have either 0 or 1 or 2 as each of its two digit, but making sure that there are no two consecutive 0 in the sequence.

here are " 9 " 2-digit ternary sequence ........... (three choices for 1st digit and three choices for 2nd digit)  

But one of these 9 sequence there are consecutive 0's .... (00)  

So we eliminate this one sequence.

So, a₂ = 8

Now

let us find the recurrence relation

Fir n ≥ 3

aₙ s the number of n - digit ternary sequence with no occurrence of the consecutive 0's in them.

For the first case: if 1st digit of this n - digit ternary sequence is 1 or 2

Let assume the 1st digit of this n - digit ternary sequence is 1.  

Then for remaining n - 1 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them.

For example, we have to form a n-1-digit ternary sequence with no occurrence of consecutive 0's in them which is by definition aₙ -1

So,

The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 1 is aₙ -1.

Likewise, the number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 2 is aₙ -1.

So  

If 1st digit of this n - digit ternary sequence is 1 or 2, then the number of n - digit ternary sequence with no occurrence of consecutive 0's in them is shown as:

aₙ-1 + aₙ -1 = 2aₙ -1

For the second case: if 1st digit of this n - digit ternary sequence is 0

If 1st digit of this n - digit ternary sequence is 0, then the next digit cannot be 0 as well because that would make two consecutive 0's in the sequence Thus,

If 1st digit of this n - digit ternary sequence is 0, the next term can be either 1 or 2.

So there are 2 choices for 2nd digit.  

After this there are more n-2 digits.  

Then

For remaining n - 2 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them  

For example, we have to form a n-2-digit ternary sequence with no occurrence of consecutive 0's in them. which is by definition aₙ - 2.

Now,

The total number of sequence in this case is given as:

2aₙ -2........... (2 choices for 2nd digit and aₙ - 2 choices for remaining n-2 digit)

Hence  

The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 0 is aₙ = 2aₙ - 1 + 2aₙ -2 which is n≥ 3

Now,

The recurrence relation for aₙ is shown below:

aₙ = 2aₙ - 1 + 2aₙ -2; is n≥ 3

With the initial conditions as a₁ =3; a₂ = 8

Answer:

[See Below]

Step-by-step explanation:

Point slope form is: [tex]y-y_1=m(x-x_1)[/tex]

'm' is the slope

(x1, y1) is a coordinate point.

Slope is rise over run. [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

We are given the points (-1,5) and (3,-3).

[tex]\frac{-3-5}{3-(-1)}=\frac{-8}{4}= -2[/tex]

The slope of the line is -2.

I will use (-1,5) as the point:

[tex]y-y_1=m(x-x_1)\rightarrow\boxed{y-5=-2(x+1)}[/tex]

Slope intercept is: [tex]y=mx+b[/tex]

'm' - Slope

'b' - y-intercept

We can use the point slope equation to convert it into slope intercept form:

[tex]y-5=-2(x+1)\\\\y-5=-2x-2\\\\y-5+5=-2x-2+5\\\\\boxed{y=-2x+3}[/tex]

Standard form is [tex]Ax+By=C[/tex]

Using out slope intercept form equation:

[tex]y=-2x+3\\\\y+2x=-2x+2x+3\\\\1y+2x=3\\\\\boxed{2x+1y=3}[/tex]

Answer:

Jomo Kenyatta

Step-by-step explanation:

Jomo Kenyatta was a Kenyan politician, who was one of the first African anti-colonial figures. He became the prime minister of Kenya from 1963 to 1964, and after Kenyan independence in 1964, he became president of Kenya. Jomo Kenyatta was born into a family of Kikuyu farmers in Kiambu, present day Kenya which was then, British East Africa. He had his basic schooling in a missionary school before proceeding to study at Moscow's Communist University of the Toilers of the East, University College London, and the London School of Economics.

Answer:

Jomo Kenyatta

Step-by-step explanation:

took the test

Answer:

equation: y = 3x + 14

number of coins after 30 months: 104 coins

Hope this helps :)

An equation is formed of two equal expressions. The number of coins that will be with Deandre after a period of 30 months is 104 coins.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

As it is given that in the initial phase Deandre saves 14 coins. While he adds 3 coins each month. Therefore, the equation that will represent the number of coins that Deandre will have after a period of x months can be written as,

y = 14 + 3x

where y is the number of coins and x is the number of months.

After a period of x=30 months, the number of coins that will be with Deandre can be written as,

[tex]y = 14 + 3x\\\\y = 14 + 3(30)\\\\y = 104[/tex]

Thus, the number of coins that will be with Deandre after a period of 30 months is 104 coins.

Learn more about Equation:

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Answer:

Step-by-step explanation:

When the time is 3:40pm

(a)The angle between the two hands in standard position is drawn and attached below.

(b)Now, each hour = 30 degrees

Therefore, the angle between 3 and 8 in an anticlockwise movement

= 7 X 30 =210 degrees

Stating the angle as a negative angle, we have:

[tex]210^\circ-360^\circ=-150^\circ\\$The angle as a negative angle is -150^\circ[/tex]

Step-by-step explanation:

[tex]( {n}^{3} )^{2} = {n}^{6} = n \times n \times n \times n \times n \times n [/tex]

Answer:

n x n x n x n x n x n

Step-by-step explanation:

(n^3)^2 = n^6 = n x n x n x n x n x n

Answer:

Degree: 4; Type: quartic; Leading coefficient: 1

Step-by-step explanation:

Answer:

[tex]x\le \:9[/tex]

Step-by-step explanation:

[tex]5x\le 45[/tex]

[tex]\frac{5x}{5}\le \frac{45}{5}[/tex]

[tex]x\le \:9[/tex]

Answer:

B

Step-by-step explanation:

We divide the entire inequality by 5 to get rid of the coefficient of x. The ≤ stays the same so we get x ≤ 9.

Answer:

See attached

Step-by-step explanation:

Given the numbers 1,2,3,4 and 5

Let O be the event that the number is Odd

Let E be the event that the number is Prime

Then the intersection of Odd and Prime Numbers: [tex]O \cap P =\{3,5\}[/tex]

Since 4 is neither odd nor prime, we place it outside of the two circles.

See the attached diagram for the required Venn diagram.

Option D is the correct answer.

Answer:

D. ∠B and ∠C are congruent.

Step-by-step explanation:

Since, ∠A and ∠B are supplementary.

Therefore,

∠A + ∠B = 180°.....(1)

Since, ∠A and ∠C are supplementary.

Therefore,

∠A + ∠C = 180°.....(2)

From equations (1) & (2)

∠A + ∠B = ∠A + ∠C

=> ∠B = ∠C

Hence, ∠B and ∠C are congruent.

Answer:

He has  2,772 ways

Step-by-step explanation:

Hello,

the teacher has to choose 6 students and there are 11 students in total.

When he chooses the first student he has 11 choices

if he has to choose 1 students he has 11 ways to do it

then for the second one he has 11-1=10 choices

if he has to choose 2 students he has (11*10)/2 ways to do it (we do not count the duplicate - for instance if he chooses Steve and then Nils or Nils and then Steve this is only one group (Steve, Nils) we do not care of the order)

Then for the third student he has 10-1=9 choices

if he has to choose 3 students he has (11*10*9)/(2*3) ways to do it (we do not take into account the order of ppl in the group)

and so on and so forth

...

if he has to choose 6 students he has (11*10*9*8*7*6)/(2*3*4*5)

so he has  2,772 ways

Answer:

C. 462 is correct. I did the test.

Step-by-step explanation:

Question Correction

Evelyn packed this box with 1 inch cubes. Which expression does not show how Evelyn can find the volume of the box?

Answer:  

(C) 2 + 3 + 6

Step-By-Step Explanation

In the diagram,  

Volume  = Height X Length X Width

= 6 X 2 X 3

=36 cubic units

Consider the options:

(A)6+6+6+6+6+6 =36 cubic units

(B) 2 X 3 X 6 =36 cubic units

(C) 2 + 3 + 6 = 11 cubic units

(D) 6 X 6 =36 cubic units

Out of the option, that which is not equivalent to 36 cubic units is:

(C) 2+3+6

Therefore, it does not show how Evelyn can find the volume of the box.

Answer:

2+3+6

Step-by-step explanation:

i just did it

Answer: 35%

Step-by-step explanation:

If no is 10, 10 x 0.65 = 6.5. OR

10 - 35% of 10 = 6.5

  Multiplying by 0.65 is the same as decreasing by 35%

Let the number is 'a' and percentage decrease is 'b',

Expression for the given statement will be,

a × 0.65 = a - (b% of a)

[tex]0.65a=a(1-\frac{b}{100})[/tex]

[tex]0.65=1-\frac{b}{100}[/tex]

[tex]\frac{b}{100}=1-0.65[/tex]

[tex]b=100(0.35)[/tex]

[tex]b=35[/tex]

    Therefore, Multiplying by 0.65 is the same as decreasing by 35%.

Learn more about the Algebraic expressions for the statements here,

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