a box contains 12 batteries of which 6 are still working. anne starts picking batteries one at a time from the box and testing them. find the probability that she has to pick 5 batteries in order to find one that works.

a. The equation in a point-slope form that represents distance as a function of time is  (y - 6)= (1/5)(x - 30).

b. The slope and y-intercept are (1/5) and 0 respectively.

c. In 4 hours I can bike for 40 miles.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know the equation of a line in point-slope form is (y - y₁) = m(x - x₁).

Given, x represents time in minutes and y represents the distance in miles.

Let us take two ordered pairs (30, 6) and (40, 8).

Slope(m) = (y₂ - y₁)/(x₂ - x₁).

Slope(m) = (8 - 6)/(40 - 30).

Slope(m) = 2/10.

Slope(m) = 1/5.

∴ The equation of the line that represents distance as a function of time

is (y - 6)= (1/5)(x - 30).

Let y = mx + b.

6 = (1/5)30 + b.

6 = 6 + b.

b = 0.

So, y-intercept(b) = 0 and slope(m) is 1/5.

I can bike in 4 hours or (4×60) = 240 minutes is,

y = (1/5)(240) + 0.

y = 48 miles.

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Answer:

The slope is 2/3

Step-by-step explanation:

y is 4 and x is 6 so it will be 4/6 then divide 2

4:2 = 2

6:2 = 3

2/3

Answer:

5 is > -4

Step-by-step explanation:

5 is greater than or equal to -4

i think this is the answer

Line g pae through point (9, 9) and (1, 4) and the slope of line h is 0.68.

The coordinates of line g are (9,9) and (1,4).

Substitute the values in the slope formula with (x1, y1) = (9,9) and (x2, y2) = (1, 4).

m = (y2-y1)/(x2-x1)

m = (4-9)/ (1-9)

m = (-5)/ (-8)

m = 0.68

the slope of the line g is 0.68

line h is parallel to line g so parallel lines have the same slope

slope of line h is 0.68

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Answer:

part A= 3

Part B= 15$

Step-by-step explanation:

Part A= 10-7=3
Part B = 5*10 =50 7*5= 35 50-35= 15$

Answer:

rise/run

(10-g)/(2-0) must equal 6

(10-g)/2 = 6

10-g = 12

-g = 2

g = -2

0.0912   is the probability that the score will be 120 or higher .

What is probability explain with an example?

Zlower = X₁ - μ/σ  = 120 - 100/15  = 1.33

the probability is compared as

                    Pr ( X ≥ 120 ) = Pr(X - 100/15 ≥ 120 - 100/15)

                                         = Pr(Z ≥ 120 - 100/15

                                          = Pr( Z ≥ 1.33)

                                          = 0.0912

Since 0.0912 > 0.05 i.e. this IQ score is not unusual and hence I can believe the claim.

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Answer:

Step-by-step explanation:

0.0010928961748634

but 50,325 divided by 55 is 915

The number of hardcover books is 24 and the number of the softcover book is 36.

Here we have to find the number of hardcover and softcover.

Here it is given that 60 books are there.

Let x be the number of hardcovers, so the number of software books is 60- x.

The weight of each hardcover is 26 ounces and of softcover is 12 ounces.

The total weight is 1056 ounces.

So we get:

26x + ( 60 -x) 12 = 1056

26x - 12x + 720 = 1056

14x = 336

x = 24

60-x = 60 -24 = 36

Therefore the number of hardcovers is 24 and the number of softcovers is 36.

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The complete question:

There are 60 books that are either hardcover or softcover. The hardcover books each weigh 26 ounces. The softcover books each weigh 12 ounces. The books weigh 1,056 ounces in all. Find the number of hardcover and softcover books are there.

Answer:

18/7

Step-by-step explanation:

check this might work as I simply

The Area of the rectangle is 32 square units

The area of the rectangle can be defined as 'the region covered by the rectangle in a 2-D plane. The formula for the area of the Rectangle or the Quadrilateral with vertices is given below

Area of Quadrilateral  

= (¹/₂) | x₁y₂+ x₂y₃+ x₃y₄ +x₄y₁ - (x₂y₁ +x₃y₂ +x₄y₃ +x₁y₄) |  

Where (x₁, y₁); (x₂, y₂); (x₃, y₃) and (x₄, y₄) are vertices of the quadrilateral

Here we have        

Vertices of rectangle are A(-1, 11), B(7, 9), C(10, 13) and D(2, 7)  

If we draw the given vertice in a graph then the order of the sides will be 'ACBD'  [ For more understanding observe the given figure ]

From the above formula,

Area of rectangle

= (¹/₂) | (-1)(13) + (10)(9) + (7)(7) + (2)(11) - [ (10)(11)+(7)(13) +(2)(9) +(-1)(7) ] |  

= (¹/₂) | -13 + 90 +49 + 22 - [ 110+ 91 + 18 - 7 ] |  

= (¹/₂) | -13 + 90 +49 + 22 - [ 110+ 91 + 18 - 7 ] |  

= (¹/₂)(64)

= 32 Square units  

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Answer:

u : -7

So the points are (0,-4) and (-7,-5)

Slope: 1/7

Step-by-step explanation:

what does it mean for an object to stay at the same height ?

come on, you cannot tell me you don't understand this.

it means that e.g. the object is at a certain height (e.g. 50 ft above the ground) at the beginning of a time interval. then 1 seconds later it is still at the same height. 1 seconds after that it is still at this height. and so on.

how do you think that shows on a chart that displays height on an up or down scale ? as a flat (horizontal) line.

the chart is simply a rough picture of what the object does in real life.

so, where do we have flat (horizontal) segments in the curve ?

between second 2 and second 6.

and then infinitely after second 12.

in interval notation

[2, 6] and [12, +infinity)

please note the round bracket on the infinity side. it means the indicated end of the interval is not included. that is, because infinity is just a concept and not a number. it can never be reached. and it is therefore not included in the interval itself.

FYI - the flat line between second 2 and second 6 is not possible in real life, unless it rolls on a flat surface or something is holding it steady in place for these 4 seconds.

but a flying ball can never have a pure flat curve regarding height. only when it comes at rest on the ground. gravity would not allow that. not even for a bullet shot by a gun.

Answer: nothing it’s a variable

Answer:

(a) 2x + x + 39 = 90

(b) m<1 = 34°; m<2 = 56°

Step-by-step explanation:

Use the angle addition postulate. Angles 1 and 2 add to a right angle. A right angle has a measure of 90°.

(a) m<1 + m<2 = 90

2x + x + 39 = 90

(b)

Solve the equation for x.

2x + x + 39 = 90

3x = 51

x = 17

Use the value of x to find the angle measures.

m<1 = 2x = 2(17) = 34

m<2 = x + 39 = 17 + 39 = 56

Answer:

a.) 3x+39=90

b.) ∠1=34°

    ∠2=56°

Step-by-step explanation:

According to the graph, ∠1 + ∠2=90°.

∠1=2x and ∠2=x+39

So,

[tex]2x+(x+39)=90\\2x+x+39=90\\3x+39=90\\3x=51\\x=17[/tex]

Rewrite the equations for the two angles substituting 17 for x.

∠1=[2(17)]°=34° and ∠2=[(17)+39]°=56°

The number of feet for the fencing needed for the entire animal pen will be 36 feet. Then the correct option is C.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

In a computer game, Shar needs to construct a pen molded like a right triangle for her creatures. Assuming she wants 9 feet of wall for the most limited side and 15 feet of wall for the longest side.

Then the third side of the triangle is given as,

⇒ √(15² - 9²)

⇒ √(225 - 81)

⇒ √144

⇒ 12 feet

Then the perimeter of the triangle is given as,

P = 9 + 12 + 15

P = 36 feet

The number of feet for the fencing needed for the entire animal pen will be 36 feet. Then the correct option is C.

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Answer: 36

Step-by-step explanation: srry if wrong i used this online calculator

In the expression (-6)⁴, the power and exponent is 4

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the power or exponents us the number of times the number is raised which is 4.

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Answer:

ofco 1+1=2

Step-by-step explanation:

abc that's why

Answer:

y = 2

Step-by-step explanation:

x + y = 8

6 + y = 8  Subtract 6 from both sides of the equation

y = 2

The cold water faucet will fill the tub on its own in 5.6 minutes.

Let us assume the time taken by cold water faucet to fill the tub be x minutes. Now, the rate of hot water faucet to fill the tub = 1/14

Combined rate of filling by both faucets = 1/4

Rate of filling by hot water faucet + Rate of filling by cold water faucet = Rate of filling of tub by combination of two faucets

1/14 + 1/x = 1/4

1/x = 1/4 - 1/14

1/x = (14 - 4)/(4×14)

1/x = 10/56

x = 56/10

x = 5.6 minutes

Thus, cold water faucet will take 5.6 minutes.

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The complete question is -

Left on together, the cold and hot water faucets of a certain bathtub take 4 minutes to fill the tub. if it takes the hot water faucet 14 minutes to fill the tub by itself, how long will it take the cold water faucet to fill the tub on its own?

John is taller then Ryan, John is 0.08 feet taller then Ryan when John is 5 1/3 feet tall, whereas Ryan is 5 1/4 feet.

Given that,

John is 5 1/3 feet tall, whereas Ryan is 5 1/4 feet.

We have to find who is tall and how much is tall.

A fraction that has the numerator higher than or equal to the denominator is said to be improper.

Take the Ryan,

5 1/4 feet

21/4 feet

5.25 feet tall Ryan.

Take the John,

5 1/3 feet

16/3 feet

5.33 feet tall John.

We can see that John is taller then Ryan.

John is 0.08 feet taller then Ryan.

Therefore, John is taller then Ryan, John is 0.08 feet taller then Ryan when John is 5 1/3 feet tall, whereas Ryan is 5 1/4 feet.

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The scatterplot and their corresponding correlation coefficient are as follows;

Scatterplot [tex]{}[/tex]                              Correlation coefficient

Scatterplot A [tex]{}[/tex]                           r = -0.42

Scatterplot B  [tex]{}[/tex]                          r = -0.85

Scatterplot C [tex]{}[/tex]                           r = 0.64

Scatterplot D  [tex]{}[/tex]                          r = 0.86

The correlation coefficient is an indication of the strength of a linear relationship that is used to model an observed dataset.

The value of the correlation coefficient ranges from -1 to 1, with a positive correlation indicating that both variables increases proportionately, and a negative correlation indicating that as one variable increases the other decreases.

A low value of the correlation coefficient indicating that there is a weak relationship between the variables such that the prediction of the output from the input has a low reliability.

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The correlation coefficients that matches the scatterplots are as follows;

Scatterplot A; r = -0.42

Scatterplot B; r = -0.85

Scatterplot C; r = 0.64

Scatterplot D; r = 0.86

The correlation coefficient is defined as a statistical measure of the strength of a linear relationship that exists between two variables. Its' values can range from -1 to 1.

Now, a correlation is considered to be a positive correlation when both variables increases or decreases in tandem which is the same direction. Meanwhile, a negative correlation is defined as on whereby one variable increases as the other decreases.

Now, the farther away the data points are from each other the greater the value of the correlation coefficient and vice versa.

The scatterplot A is a negative correlation because the output increases as the input decreases and vice versa. This is more scattered than the other negative correlation; r = -0.42

The scatterplot B also has a stronger negative correlation than scatter plot A since r = -0.85

The scatterplot C has a positive correlation, but not so strong as seen by the spacing of the scatter dot points. Thus, the scatterplot C has a correlation coefficient of r = 0.64

The scatterplot D has a stronger positive correlation coefficient than C as seen in the dot scatter points and as such its' correlation coefficient is 0.86

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Answer:  Total distance 2√10

Step-by-step explanation:

The distance from coordinates p (5, 7) to coordinates (–2, 1) and (4, 1) in line n are  9.21 units and 6.08 units respectively.

The distance between two points is defined as the length of the line segment between two places representing their distance.

The distance from coordinates p (5, 7) to coordinates (–2, 1) in line n will be

⇒ √[(-2-5)² + (1-7)²]

⇒ √[(-7)² + (-6)²]

⇒ √[49 + 36]

⇒ √85

⇒ 9.21 units

The distance from coordinates p (5, 7) to coordinates (4, 1) in line n will be

⇒ √[(4-5)² + (1-7)²]

⇒ √[(-1)² + (-6)²]

⇒ √[1 + 36]

⇒ √37

⇒ 6.08 units

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Answer: x ≈ 2.67

Step-by-step explanation:

    To solve, we will isolate the variable with reverse operations.

    Given:

[tex]\displaystyle x^2=\frac{521}{73}[/tex]

    Square root both sides of the equation:

[tex]\displaystyle x=\sqrt{\frac{521}{73}}[/tex]

    Evaluate:

x = 2.6715138 ... ≈ 2.67

The area of the field is 4140 square yards.

A rectangle is a quadrilateral with all four interior angles 90°.

Given that, the perimeter of the field is 302 yards.

Let the length and width of the field be l and w respectively.

Given that, the length is 7 yards longer than three times its width, therefore,

l = 7 + 3w

The perimeter of the field is given by:

2(l +w) =302

l + w = 151

w = 151 - l..........(1)

Substitute l = 7+3w into the above equation:

w = 151 - 7 - 3w

w + 3w = 144

4w = 144

w = 36

Substitute w = 36 into equation (1):

36 = 151 - l

l = 151 - 36

l = 115

The area of the field is:

l × w

115 × 36

=4140

Hence, the area of the field is 4140 square yards.

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A statement that explains whether 0.1515 is rational: Yes, because 0.1515 is a repeating decimal, so it can be expressed as a ratio of integers.

The correct answer is an option A

We need to select a correct statement that explains whether 0.1515 is rational.

We can observe that 0.1515 is the recurring decimal 0.15

This decimal can be written as a ratio of two integers.

Consider numerator = 5 and the denominator = 33.

So, 5/33 = 0.1515..

This means, 0.1515 can be expressed as p/q where p, q are integers with q ≠ 0

Therefore, a statement that explains whether 0.1515 is rational: Yes, because 0.1515 is a repeating decimal, so it can be expressed as a ratio of integers.

The correct answer is an option A

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Answer:

  (d)  Yes, it is proportional because the farmer collected 180 bushels for every 1 acre harvested.

Step-by-step explanation:

You want to know if the ratios 4 acres : 720 bushels and 7 acres : 1260 bushels represent a proportional relationship.

A relationship is proportional if the ratio of the dependent variable to the independent variable is a constant. We can check this for the numbers given:

  (720 bu)/(4 ac) = 180 bu/ac

  (1260 bu)/(7 ac) = 180 bu/ac

The ratios are the same, 180 bushels for each acre, so the relationship is proportional.

Answer:

 (d)  Yes, it is proportional because the farmer collected 180 bushels for every 1 acre harvested.

Step-by-step explanation:

I took the exam and got it right

Answer:

-8 and then the second one is -11

Step-by-step explanation:

Answer:

Step-by-step explanation:

it’s negative 3

The number of boxes that the delivery person can carry at a time is less than or equal to 15.

Given,

The weight of the delivery person = 160 lb

The weight of one box of books he carries = 60 lbs

The maximum capacity of the elevator = 1110 lb

We have to find the number of boxes of books can the delivery person bring up at one time;

Let x be the number of boxes;

Then,

The number of boxes that the delivery person can carry at a time;

160 + 60x ≤ 1110

60x ≤ 1110 - 160

x ≤ 950/60

x ≤ 15.8

That is,

The number of boxes that the delivery person can carry at a time is less than or equal to 15.

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