What is the converse of the conditional statement "If the streetlights are on, then the sun has gone down."?
O If the sun has gone down, then the street lights are on.
O If the streetlights are not on, then the sun has gone down.
O If the streetlights are not on, then the sun has not gone down.
If the sun has not gone down, then the streetlights are on.

∠1≅∠3 line 2 and 3 have the same reason.

∠1 and ∠3 are vertical angles, so they are formed by intersecting lines. Therefore ang1 and ∠2 are a linear pair, and ∠2 and ∠3 are a linear pair. By the Linear Pair Theorem, ∠1 and ∠2 are supplementary, and ∠2 and ∠3 are supplementary. So by the Congruent Supplements Theorem, ∠1 ≅ ∠3.

Statements  - Reason

1. ∠1 and ∠3 are vertical angles  -  Given.

2. a and b are intersecting lines  -  definition of vertical angles

ang1 and ∠2 are a linear pair

3. ∠2 and ∠3 are a linear pair  -  definition of a line

4. ∠ 1 and 2 are supplementary ang2 and ang3 are supplementary - definition of linear pair.

5. ∠1 ≅ ∠3  -  ≅ Supplements theorem

Hence the answer is ∠1≅∠3 line 2 and 3 have the same reason.

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The equation is y = -3

Since, the line parallel to the line y=5, its slope is zero.

so, the equation has the form

y = constant

it passes through (-2,-3), the equation is

y = -3

Slope of a Line :

In mathematics, a line's slope is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

The net change in the y-coordinate and the net change in the x-coordinate are denoted by the letters Y and X, respectively.

Since the slope of a line is denoted by "m," the formula for the change in y-coordinate with respect to the change in x-coordinate is m = change in y/change in x = y/x.

The slope, intercept, and y-intercept values on the graph of the equation y = mx + c are all equal to m. M and C are real integer values in the slope-intercept version of the linear equation.

Complete question:

find an equation of the line parallel to the line y=5 and passing through -2,-3

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Answer: 89.75

Step-by-step explanation:

So 392.50 is the cost of 2 phones and 6 headphones and 286.00 is the cost of 2 cell phones and three headphones. so 392.50-286.00 is the cost of 3 headphones since you added three headphones to the price. so the price of 3 headphones is 106.50. Then you subtract 106.50 from 286.00 to get the cost of the two cell phones. And you get 179.50. Then, you divide 179.50 in order to get the price of one cell phone and you get 89.75. So the cost of one cell phone is $89.75.

Answer: The correct answer is B.

Step-by-step explanation:

In a line with a slope of 0 the x can change but the y cannot in a (x, y).

According to the Symmetric Property of Equality, if AB = CD then CD = AB.

According to the question,

We have the following information:

CD = AB then AB = ?

Now, in order to fill the given blank, we have to use the symmetric property of equality. According to the symmetric property of equality, there is no difference in the final result of an expression if we change the sides of the expression.

For example, if 2 = a then we can also say that a = 2.

So, when CD=AB then we can clearly state that AB = CD.

Hence, according to the Symmetric Property of Equality, if AB = CD then CD = AB.

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After the conversion, 133 hours and 33 minutes will it take to completely empty the pool which contains 12,000 gallons.

In the given question we have to find how many hours and minutes will it take to completely empty the pool which contains 12,000 gallons.

As given that pool empties at a rate of 12 quarts every 2 minutes.

In 12 quarts = empties in 2 minutes

As we know that 1 gallon = 4 quarts

So 1 quarts = 1/4 gallon

In 12 quarts = 12/4 gallon

12 quarts = 3 gallon

So 3 gallon = empties in 2 minutes

So 1 gallon = empties in 2/3 minutes

12,000 gallon = empties in 2/3 ×12,000 minutes

Simplifying

12,000 gallon = empties in 2×4,000 minutes

12,000 gallon = empties in 8,000 minutes

Now converting minutes in hours.

As we know that 1 minute = 1/60 hours

So 8000 minute = 8000/60 hours

8000 minutes = 133 hours 33 minutes

133 hours and 33 minutes will it take to completely empty the pool which contains 12,000 gallons.

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He collected 936 US stamps.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Total number of stamps - 1170

US stamps - 4 times as many as foreign stamps

Let x be the number of foreign stamps.

4x as the number of US stamps.

To find the number of US and foreign stamps Peter collected, we are going to represent the given data as:

x + 4x = 1170.

x + 4x = 1170

5x = 1170

5x/5 = 1170/5

x = 234

Peter collected 234 foreign stamps.

US stamps = 4x

= 4(234)

= 936

Peter collected 936 US stamps.

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Answer:Let the age of son be x.

Thus, age of father is 4x.

After 5 years, their ages will be x+5 and 4x+5 years respectively.

As per the question, we have

4x+5=3(x+5)

⇒4x+5=3x+15

⇒x=10

Age of father will be 4x=4×10=40 years.

Thus when son is 10 years old, father is 40 years.

Step-by-step explanation:

After 3 years father's age will be five times that of his son. Father age will be 40 years and son age will be 8 years .

Given,

Present age of father = 37 years.

Present age of son = 5 years.

Now,

Let the number of years be x after which the fathers age will be 5 times the age of his son.

So,

Ages after 3 years  ,

Age of father = 40 years

Age of son = 8 years.

Thus age of father is 5 times the age of son.

Therefore after 3 years father's age will be five times that of his son.

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Answer:

y= 50x + 200

Step-by-step explanation:

a) The linear equation that represents the total amount of snow, y, after x number of hours is: y = 2 + 0.25x.

b) 3 inches is the amount of snow that is on the ground after four hours.

c) The time until the snow reaches 6 inches is of 16 hours, which is enough to finish the hike, as they usually take at most five hours.

The slope-intercept representation of a linear function is shown by the equation as follows:

y = mx + b

In which the parameters m and b of the linear equation are explained as follows:

Thus the values of these parameters are given as follows:

m = 0.25, b = 2.

The equation that represents the total amount of snow, y, after x number of hours is:

y = 0.25x + 2.

The numeric value of function after four hours is found replacing the lone instance of x on the function by 4, hence:

y = 0.25(4) + 2 = 3 inches.

To find when the amount will be of six inches, we have to solve for x when y = 6, hence:

2 + 0.25x = 6

0.25x = 4

x/4 = 4

x = 16 hours.

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Answer:13234

Step-by-step explanation:

13234 is

Step-by-step explanation:

[tex]3g = d[/tex]

[tex] \frac{3g}{3} = \frac{d}{3} \\ [/tex]

[tex]g = \frac{d}{3} \\ [/tex]

[tex]{ \purple{ \bold{g = \frac{d}{3}}}} [/tex]

Step-by-step explanation:

The given formula is [tex]{ \orange{ \sf{3g = d}}}[/tex]

In order to get formula for g, let us divide 3 on both the sides.

[tex]{ \orange{ \sf{ \frac{ \cancel3}{ \cancel3}g}}} = { \orange{ \sf{ \frac{d}{3}}}} [/tex]

Therefore, [tex]{ \boxed{ { \tt{g = \frac{d}{3}}}}} [/tex]

Answer:

Step-by-step explanation:

I'm impressed that they make you do this in H.S.    Linear Algebra.   it's good for more complex math .   so that's why i'm impressed.   Is this an AP class?  

Ax=B is our formula.   we need to know something about x,  it's size

so we look at rows and columns of A,   2x2   , also we need to know about B as well it's also 2x2

so now we know, that   a matrix  A, of  size  2x2,  *x = B of size 2x2

2x2*x=2x2   ....   2x2|2x2   since the two inside number match, we can do this multiplication,  and the two ouside numbers tell us the size of  x... it's also a 2x2.  I know, a lot of explaining to just get 2x2.   Maybe that is obvious, and i'm mansplaining,  :DD  ,  but I don't know what you know.

I'll put big subscripts on my matrix variable so you can see it well.  You understand the subscript is the element location in the matrix , right?  1,1 is just the top left corner element of the matrix.  ect , ect.

so now we need,  a1,1 * x1,1 + a1,2 * x2,1   = 2  in b1,1

then we need   a2,1 * x1,1 + a2,2 * x2,1 = 7  in b2,1

next we need a1,1 * x1,2 + a1,2 * x2,2   = 3  in b1,2

finally we need a2,1 * x2,1 + a2,2 * x2,2   = 8  in b2,2

X =  [tex]\left[\begin{array}{ccc}\frac{3}{2} &1\\\frac{1}{2} &2\end{array}\right][/tex]   I did that by observation.   have you learned any RREF methods yet?

Using distributive law and the greatest common factor , the expression (32 + 16) can be factored as 16(2 + 1)

The GCF(greatest common factor) is defined as the largest number that is a factor of two or more numbers.

In a simpler term, the greatest number among all the common factors of two or more numbers is called the greatest common factor or GCF.

Using distributive law and the greatest common factor we can factor an expression.

Therefore, let's factor the expression (32 + 16).

The greatest common factor of 32 and 16 is 16.

Therefore, the expression can be express as follows:

(32 + 16) = 16(2 + 1)

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The area of each of the patios is 1600 m².

The mason builds two patios with the same area. One of the patios is square, and the other is rectangular. The rectangular patio is 10 m longer but 8 m less wide than the square patio. We need to find the area of each patio.

Let the side length of the square patio be denoted by the variable "x". The area of the square can be calculated as follows.

A1 = x²

The length and breadth of the rectangular patio is "x + 10" and "x - 8", respectively. The area of the rectangular patio is calculated below.

A2 = (x + 10)*(x - 8)

A2 = x² + 2x - 80

We know that the areas of both patios are equal.

A1 = A2

x² = x² + 2x - 80

2x = 80

x = 40

Hence, the area of each patio is A = x² = 40² = 1600 m².

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The equation represents the line that passes through the points (6, -12) and (16,-10) is y = 1/5x - 13.2

The first point = (6, -12)

The second point = (16, -10)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line m = (-10 -(-12) / (16 - 6)

= (-10 +12) / 10

= 2/10

= 1/5

The slope intercept form is

y = mx + b

Consider the point (6, -12)

-12 = (1/5)6 + b

-12 = 6/5 + b

b = -12 - 6/5

b = -13.2

The equation will be

y = 1/5x - 13.2

Hence, the equation represents the line that passes through the points (6, -12) and (16,-10) is y = 1/5x - 13.2

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Answer:

35

Step-by-step explanation:

y = 25 and x = 5

When two variable quantities have a constant ratio their relationship is called a direct variation. The formula for direct variation is y = kx, where k is called the constant of variation.  If we know k we can find y given x or we can find x given y.

If we solve the equation y = kx for k, we get k = y/x.  If we replace the variables x and y with the actual values from the problem we have:

k = 25/5, which is 5.  

Now we can substitute this value for k into the equation y = kx to find y when x is 7:

y = (5) (7)

y = 35

There are 20 players are not in 5th grades.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

Total players in the class = 80

And, 75% of the players in the basketball program are 5th graders.

Now.

Number of players in the basketball program are 5th graders = 75% of 80

= 75/100 x 80

= 60

Thus, Number of players are not in 5th graders = 80 - 60

                                                                          = 20

Therefore, There are 20 players are not in 5th grades.

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Answer:

145°

Step-by-step explanation:

Answer: y equals 145 degrees

The approximate probability that a 47% shooter makes 5 or more shots in 10 attempts is 12/25

Given,

Number of trials of the simulation were performed = 25

Number of set of simulated shots = 10

We have to find the approximate probability that a 47% shooter makes  5 or more shots in 10 attempts;

The dots in the 5 shot mark is 9, 6 shot mark is 2, and 7 shot mark is 1.

Now the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts can be calculated below:

P(x5) = (dots in 5 short mark + dots in 6 shot mark + dots in 7 short mark) / 25

= (9 + 2 + 1) / 25

 = 12 / 25

Therefore, the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts is 12/25

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Answer: ( 4 , 8 )

Step-by-step explanation:

3x - 2y = -4

y = 2x

Substitute the second equation into the first

3x - 2(2x) = -4
3x - 4x = -4
-1x = -4
x = 4

y = 2(4)
y=8

( 4 , 8 )

According to the two tailed test, the difference between the first and second country is 40.

Two tailed test:

Two tailed test also means the two-sample t-test is used to determine if two population means are equal.

Given,

Let p1 and p2 be the respective proportions of women with iron-deficiency anemia in each of two developing countries. a random sample of 1800 women from the first country yielded 392 women with iron-deficiency anemia, and an independently chosen, random sample of 1700 women from the second country yielded 352 women with iron-deficiency anemia.

Here we need to find the the proportion of women with anemia in the first country differs from the proportion of women with anemia in the second country.

While we looking into the given question,

For the first country,

Number of samples = 1800

Number of women with iron-deficiency anemia = 392

And for the second country,

Number of samples = 1700

Number of women with iron-deficiency anemia = 352

So, there difference between them is calculated as,

=> 392 - 352

=> 40

And as per the two tailed test both countries doesn't have the same proportion and the sample values is also differs this situation.

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Answer:40

Step-by-step explanation:

so 14 less means that 14 was subtracted. So we need to add that to our main number, 66. When we do that we get 80. Then since 80 is twice the number we are looking for, we divide by 2 (twice is 2 times), and we get 40. Hope this helps

The choice that best represents David monthly interest rate is 0.625%. The correct option is C.

From the information, David opens a savings account with a 7.5% annual interest rate.

It should be noted that there are 12 months in a year.

Therefore, the monthly interest rate will be:

= Annual interest rate / Number if months in a year

= 7.5% / 12

= 0.625%

The interest is 0.625%.

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Complete question

David opens a savings account with a 7.5% annual interest rate. Which choice best represents his monthly interest rate?

A. 7.5%

B. 12%

C. 0.625%

D. 5%

Answer:

lo siento soy muy malo para las matemáticas y además soy nuevo en este aplicación

Answer:

120[tex]ft^{2}[/tex]

Step-by-step explanation:

4 yards is 12 feet

10(12) = 120

Answer:

120 square feet

1 ) We first need to convert the 4 yards into feet...

1 yard = 3 feet

so 4 yards = 12 feet

2 ) To find area we do length x width...

length = 10

width = 12

10 x 12 = 120

( 120 square feet )

Hope this helps! :)