Dean asked his classmates, "How many apples did you eat last week?" He got the following responses: 7, 5, 5, 5, 7, 3, 2, 1, 0, 0, 4, 3, 2, 1, 0, 7, 5, 6, 7, 0, 2, 2, 1, 4. Make a line plot to display the data​

The equation of the line given in the graph will be:

2y = -3x +2

Given line is passing through the point (2, -2), with the y-intersect of 1(From the graph).

The slope-intercept form of the equation of a line,

y=mx+b,

where m is the slope

b is the y-intercept

since, slope = (y - y')/(x -x')

In our case,

m = (-2-1)/(2-0)

m = -3/2

Thus, the equation of the line will be

y = -3/2x + 1

2y = -3x +2

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Answer:

Assuming your equations are:

x-3y=3

4x+3y=-3

The answers are x = 0 and y = -1.

See the image for the graph.

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Step-by-step explanation:

See the image for the graph.

Answer:

(0,3)

Step-by-step explanation:

Answer:

The two points- (0,3) (-2,-1)

The y-intercept is (0,3)

The slope is 2

Values of parameters n and p for the binomial distribution with mean 6 and variance 3.6 are n=15 and p=0.4, respectively.

In probability theory and statistics, the binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent and identical trials, where each trial can result in only two possible outcomes, often labeled as "success" and "failure".

The distribution depends on two parameters: the probability of success (p) and the number of trials (n). The probability of getting exactly k successes in n trials can be calculated using the binomial probability mass function.

The binomial distribution has applications in various fields, including quality control, genetics, and finance, among others.

We know that for a binomial distribution, the mean and variance are given by:

Mean = np

Variance = np(1-p)

Substituting the given values, we have:

Mean = 6

Variance = 3.6

Thus, we can write two equations:

6 = np

3.6 = np(1-p)

We can solve for n and p by substituting the first equation into the second equation:

3.6 = (6/p) * (1-p) * p

3.6 = 6 - 6p

6p = 6 - 3.6

p = 0.4

Substituting this value of p into the first equation, we get:

6 = n * 0.4

n = 6 / 0.4

n = 15

Therefore, the values of the parameters n and p are n = 15 and p = 0.4, respectively.

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Answer:

O. 10+y=4

y=4-10

y=-6

D -10 + y = 3

y=3+10

y=13

C. -11+ x = -5

x=-5+11

x=6

K -13 + a = -60

a=-60+13

a=-47

Answer:

The answer should be 210 unit cubes.

Step-by-step explanation:

The volume of a rectangular prism is given by the following expression:

\(volume = length*width*height\)

In words, it is the product of its edge lengths. If the prism was packed with 210 unit cubes, then this must be equal to its volume, so by multiplying the edge lengths the result should be equal to 210 unit cubes.

Answer: not a solution

Step-by-step explanation: 7a = 7 * 21 which does not equal 28, it equals 147, 7 * 4= 28, so actually a=4

Hope this helps :)

Neither of the segments is the perpendicular bisector of the other.

To determine which segment is the perpendicular bisector of the other, we need to find the equations of the lines containing each segment and then check if one of the lines is perpendicular to the other and passes through the midpoint of the other segment.

Let's start by finding the midpoint of segment AT. The coordinates of A and T are not given, but we don't actually need them to find the midpoint.

So, the midpoint M of segment AT is:

M = ((AT_x1 + AT_x2)/2, (AT_y1 + AT_y2)/2)

We don't know the actual values of AT_x1, AT_x2, AT_y1, and AT_y2, but we can find their expressions in terms of x using the segment lengths and the coordinates of the endpoints. We have:

AT_x2 - AT_x1 = BT_x2 - AT_x1 = (x + 5) - (2x + 3) = -x + 2

AT_y2 - AT_y1 = BT_y2 - AT_y1 = (BT - AT) = (x + 5) - (2x + 3) = x + 2

Therefore,

AT_x1 = AT_x2 + x - 2

AT_y1 = AT_y2 - x - 2

Now, we can substitute x=2 and the expressions for AT_x1 and AT_y1 into the midpoint formula to find the coordinates of M:

M = ((AT_x1 + AT_x2)/2, (AT_y1 + AT_y2)/2) = ((AT_x2 + 2 - AT_x2)/2, (AT_y2 - 2 - AT_y2)/2) = (1, -1)

So, the midpoint of segment AT is M(1, -1).

Next, let's find the equations of the lines containing segments AT and DT. We can use the point-slope form of the equation of a line, which states that the equation of a line passing through a point (x1, y1) with slope m is y - y1 = m(x - x1).

For segment AT, we have:

m_AT = (AT_y2 - AT_y1)/(AT_x2 - AT_x1) = (x + 2)/(x - 1)

Let's substitute x=2 to find the slope of the line containing segment AT:

m_AT = (2 + 2)/(2 - 1) = 4

So, the equation of the line containing segment AT is:

y - AT_y1 = m_AT(x - AT_x1)

y - (22 + 3) = 4(x - 22 - 1)

y - 7 = 4(x - 5)

y = 4x - 13

For segment DT, we have:

m_DT = tan(m∠ATD) = tan(41x + 8)

Let's substitute x=2 and simplify:

m_DT = tan(82 + 8) = tan(90) = undefined

This means that the line containing segment DT is vertical and its equation is x = DT_x1 = 4*2 + 1 = 9.

Now, we need to check if one of these lines is perpendicular to the other and passes through the midpoint of the other segment.

First, let's check if the line containing segment AT is perpendicular to the line containing segment DT.  We have:

m_AT * m_DT = 4 * undefined = undefined

Since undefined is not equal to -1, the lines are not perpendicular, and we can rule out the possibility that the line containing segment AT is the perpendicular bisector of segment DT.

Next, let's check if the line containing segment DT is perpendicular to the line containing segment AT. We have:

m_AT = 4

So, the slope of the line perpendicular to the line containing segment AT is -1/4. We can use the point-slope form of the equation of a line again:

y - M_y = -1/4(x - M_x)

y - (-1) = -1/4(x - 1)

y + 1 = -1/4x + 1/4

y = -1/4x + 3/4

Now, we need to check if this line passes through point D, an endpoint of segment DT. We can substitute the coordinates of D into the equation of the line and check if the equation holds true:

DT_y1 = 4*2 + 1 = 9

DT_x1 = 9

9 = -1/4*9 + 3/4

9 = -9/4 + 3/4

9 = -6/4

This is not true, so the line containing segment DT does not pass through point D. Therefore, we can conclude that the line containing segment DT is not the perpendicular bisector of segment AT.

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Option (B) Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour is correct.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that:

A group of hikers tracked how long it took to hike a 10-mile trail. They hiked 2.5 miles in 2 hours, 7.5 miles in 6 hours, and 8.75 miles in 7 hours.

From the data given:

Ratio = distance/time

2.5 / 2 = 1.25 miles per hour

7.5 / 6 = 1.25 miles per hour

8.75 / 7 = 1.25 miles per hour

Thus, option (B) Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour is correct.

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Answer:

Infinitely Many Solutions

Step-by-step explanation:

We can start by simplifying both sides of the equation:

2(12-w) = -2(w-17)-10

Expanding the brackets:

24 - 2w = -2w + 34 - 10

Simplifying:

24 - 2w = -2w + 24

At this point, we can see that both sides of the equation are equivalent, so we can conclude that the equation is an identity and has infinitely many solutions. Any value of w will satisfy the equation.

The storm rainfall flux is 0.00127 m2/hr, 1.27 kg liquid water/m2hr, 2.8 lb liquid water/m2hr, 1.27 liters liquid water/m2hr, and 0.335 gallons liquid water/m2hr. The amount of liquid water fell on the garden is 80.6 L, 21.3 gallons.

Dimensions of outdoor vegetable garden = 2 m × 2 m

Storm rainfall = 0.8 inches of rain

Time of storm = 1 hr(

a) The rainfall flux is the amount of rainfall per unit area and unit time. It is given as:

Rainfall flux = (Amount of rainfall) / (Area × Time)

Given the area of the garden is 2 m × 2 m, and the time is 1 hr, the rainfall flux is:

Rainfall flux = (0.8 inches of rain) / (2 m × 2 m × 1 hr)

Converting inches to meters, we get:

1 inch = 0.0254 m

Therefore,

Rainfall flux = (0.8 × 0.0254 m) / (2 m × 2 m × 1 hr) = 0.00127 m/hr

Converting the rainfall flux to other units:

In kg/hr:

1 kg of water = 1000 g of water

Density of water = 1000 kg/m3

So, 1 m3 of water = 1000 kg of water

So, 1 m2 of water of depth 1 m = 1000 kg of water

Therefore, 1 m2 of water of depth 1 mm = 1 kg of water

Therefore, the rainfall flux in kg/hr = (0.00127 m/hr) × (1000 kg/m3) = 1.27 kg/m2hr

In lbs/hr:

1 lb of water = 453.592 g of water

So, the rainfall flux in lbs/hr = (0.00127 m/hr) × (1000 kg/m3) × (2.20462 lb/kg) = 2.8 lbs/m2hr

In liters/hr:

1 m3 of water = 1000 L of water

So, 1 m2 of water of depth 1 mm = 1 L of water

Therefore, the rainfall flux in L/hr = (0.00127 m/hr) × (1000 L/m3) = 1.27 L/m2hr

In gallons/hr:

1 gallon = 3.78541 L

So, the rainfall flux in gallons/hr = (0.00127 m/hr) × (1000 L/m3) × (1 gallon/3.78541 L) = 0.335 gallons/m2hr

(b) To calculate the amount of water that fell on the garden, we need to calculate the volume of water.

Volume = Area × Depth.

The area of the garden is 2 m × 2 m.

We need to convert the rainfall amount to meters.

1 inch = 0.0254 m

Therefore, 0.8 inches of rain = 0.8 × 0.0254 m = 0.02032 m

Volume of water = Area × Depth = (2 m × 2 m) × 0.02032 m = 0.0806 m3

Converting the volume to other units:

In liters:

1 m3 of water = 1000 L of water

Therefore, the volume of water in liters = 0.0806 m3 × 1000 L/m3 = 80.6 L

In gallons:

1 gallon = 3.78541 L

Therefore, the volume of water in gallons = 80.6 L / 3.78541 L/gallon = 21.3 gallons.

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Answer:

27:3

Step-by-step explanation:

multiply the 9 by 3 to get the first part

Explanation

To get that value, we multiply every number in the ratio 9:1 by 3

9*3 = 27

1*3 = 3

Therefore, the ratio 9:1 is equivalent to 27:3

Answer: 9= -1.5 or -3/2

               10= -11/6 or 1.8333

                11= -10.9

                 12= 3.535

                   13= Town A is -3.33 Town B is -3 2/5, 2/5= .44, so town B is colder, as it is -3.44

                     14= I'm not sure about number 14, sorry about that

9.

Explanation: So for question 9, you need to find the LCD (Least common denominator) so you list out the multiples of 8 and 4, when doing so, you find out that 8 is the LCD of both, since 8 is both a multiple of itself and of 4.

So, to get the answer, you do 4 * 2 and anything you do to the denominator (bottom number), you do to the nominator (top number).

So now you have -8/3/8 +6/2/8 then you just add the nominators and whole numbers like normal. You get, -2/1/8 (Remember you are adding a positive number to a negative number.)

Answer: -2/1/8

10.

Explanation: Same process as question 9.

Answer: -4/1/12

11.

Explanation: Read -7.3 out loud, it would be negative seven and 3 tenths, that makes it easy to convert as a fraction. It would be -7/3/10. Do the same for the other number, and you have -3/6/10, then you just add. You get -10/9/10.

Answer: -10/9/10

12.

Explanation: Same process as question 11. (You're in the thousandths now.) You get 3/535/1000. Reduce.

Answer: 3/107/200

13.

Explanation: You have 2 options here, to convert the decimal into a fraction, or to convert the fraction into a decimal, I'll be changing the fraction into a decimal, you wanna write it as a 10 as a denominator, so to get to 10 you multiply the denominator by 2, and anything you do to the denominator, you do to the nominator. So, -3/2/5 as a decimal is: -3.4, then you go ahead and compare them and you can see that the temperature in town A is colder.

Answer: The temperature in town A is colder.

14.

Explanation: For this one, you just subtract or add the amount to 7number. The dates don't matter, just telling you to do it in that order.

60.68 + 75.50 = 136.18

136.18 - 25.16 = 111.02

111.02 - 82.05 = 28.97

28.97 + 59.95 = 88.92

Answer: $88.92

Step-by-step explanation:

Number of shirts she didn't fold= n

Number of shirts she folded = f

So = total number of shirts - number of shirts folded = shirts that aren't folded

= equation = 27 - f = n

= so if she folded 11, f = 11

So n = 27 - 11

So n = 16

So, 16 shirts are left to fold

Answer:

Step-by-step explanation:

Let M and S be the numbers of Math and Science books, respectively.  Let T be Steve's Total money he has to play with.

We are told that if Steve splurges (as he should) on nothing but science books. he has $6 left.

We can write this as:  7S = T - 6  [The number of science books, S, times $7 each, leaves Steve with only $6 (T - 6).]

We also find that if he buys the same number of math books, he'll need $8 more.  Zounds.  But we can write this as:  9M = T + 8  But since we know he is buying the same number as science, we can also write this as 9S = T + 8    [The same number as he bought for science, S, times $9, Steve needs another $8].

We have two equations and two unknows (S and T), so lets see if we can solve for these variables.

7S = T - 6

9S = T + 8

Let's rearrange the first:  T = 7S + 6

Now use that  vale of T in the second equation:  

9S = T + 8

9S = (7S + 6) + 8

2S = 14

S = 7  That's 7 Science books.  It's also the value of M, 7 math books, since the problem states if he bought the same number as science books.

Now use S = 7 to find T, the total money Steve has [after coffee and doughnuts].

7S = T - 6

7*7 = T - 6

T = 49 + 6

T = $55

----

Let's see if $55 works for both the science and math book options:

1.  7 Science books:  $7/(S book)*(7 books) = $49  [He has $6 left]

2.  7 Math books:  $9/(M book)*(7 books) = $63  [He needs $8 more]

These results match the problem statements.

Steve has $55 (T).  He can buy either  7 science books or 6 math books:

Math:  6*($9) = $54  with $1 left, or

Science:  7*($7) = $49 with $6 left.

I suggest 6 Science books ($42) and 1 Math book ($9) for a total of $51, and still have $3 for coffee.  We aren't told if these books are all different from one another.  If they aren't, then Steve needs to ponder why he needs duplicated books.

Answer:

10x.............

Step-by-step explanation:

or x=10

Answer:

x = 14

Step-by-step explanation:

Okay so the equation looks like this:

X/-2 = -7

In order for us to get rid of the -2 we are going to have to multiply -2 on both sides of the equal sign, so that we only have x on one side of the equal sign and numbers on the other:

X/-2 = -7

 *-2  *-2

since multiplying or dividing a negative number by a negative number gives you a positive -7 is going to become 14 and x remains on the other side of the equal sign:

x = 14

Now to check our work we are going to place 14 where the x variable is in the equation:

X/-2 = -7 or (14)/-2 = -7

-7 = -7

Hope this helps you!!

Answer: 2:3

Step-by-step explanation:

Hallie donated 4 pairs and Mattie 6

the ration is 4:6

simplify that (both can be divided by two) and you get 2:3

So for every two pairs of jeans Hallie Donates, Mattie Donates 3

Hope that helps

The ratio to describe the number of jeans shared by Hallie and Mattie is obtained as 2 : 3.

The ratio of two numbers a and b can be written as a : b = a/b.

The ratio of two quantities is the unit rate of one quantity with respect to the other.

The number of jeans donated by Hallie and Mattie are given as 4 and 6 respectively.

It can be written in terms of ratio as 4 : 6.

It can be simplified as,

⇒ 4 : 6

⇒ 4/6

⇒2/3

⇒ 2 : 3

Hence, the number of jeans donated can be written in terms of ratio as 2 : 3.

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The numerical value of x in the secant line is 4.

The Intersecting Secants Theorem states that "when secants intersects, their line segments are in proportion.

Its is expressed as:

Segment AB × segment AC = segment AD × segement AE.

From the image of the intersecting secants:

Let:

6 = segment AB

x + 6 = segment AC

5 = segment AD

5 + 7 = segment AE

Now, these values into the above formula:

Segment AB × segment AC = segment AD × segement AE.

6 × ( x + 6 ) = 5 × ( 5 + 7)

Solve for x

6x + 36 = 25 + 35

6x + 36 = 60

6x = 60 - 36

6x = 24

x = 24/6

x = 4

Therefore, the value of x is 4.

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A) If Sofi accidentally spills 5% of the container's maximum capacity on the counter, the container is now filled to 87.5% of its capacity.

B) If Sofi needs to add 16 ounces of water to her turtle tank, she needs to use 28.57% of the remaining water in the container.

Given that Sofi stores water for her turtle tank in a container with a maximum capacity of 64 ounces and the container is filled with 4.8 ounces less than its maximum capacity, to determine A) if Sofi accidentally spills 5% of the container's maximum capacity on the counter, to what percent of its capacity is the container now filled, and B) if Sofi needs to add 16 ounces of water to her turtle tank, what percentage of the remaining water in the container does she need to use, the following calculations must be made:

A)

Therefore, if Sofi accidentally spills 5% of the container's maximum capacity on the counter, the container is now filled to 87.5% of its capacity.

B)

Therefore, if Sofi needs to add 16 ounces of water to her turtle tank, she needs to use 28.57% of the remaining water in the container.

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Answer:

A=87.5%   b=28.57

Step-by-step explanation:

ADVICE PLEASE LOOK AT THIS VERY HELPFUL

PART                           percent

--------- over =          ----------------- over   Cross multiply and then divide by 100  

WHOLE                       100%

Answer:

SAS

Step-by-step explanation:

if two sides and the included angle of one triangle are congruent to two corresponding sides and the included angle of another triangle, then the two triangles are congruent.

Length is the independent variable while P is the dependent variable.

Independent variables are variables that can stand alone while dependent are depend on others.

Independent variables are input variables of a function whole independent are the output variables of a function.

Given the function as shown:

P = 2l + 20

length is the independent variable while P is the dependentw variable.

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Answer:

1:3

Step-by-step explanation:

8:24

divide by 8

1:3

Answer 1.3

hope it help!

Step-by-step explanation:

Answer:

What do you mean???

Step-by-step explanation:

Answer:

the price of the vanilla flavored coffee per pound is $8.50

the price of the espresso flavored coffee per pound is $9.00

Step-by-step explanation:

Let's give letters to the unknowns, so we can generate equations easily:

cost of espresso coffee beans per pound:  "E"

cost of vanilla flavored coffee beans per pound : "V"

Now, the first statement:

18 pounds of E plus 17 pounds of V cost $306.50, can be written as:

18 E + 17 V = 306.5

The second statement:

19 pounds of E plus 15 pounds of V cost $298.50, can be written as:

19 E + 15 V = 298.5

Now, in order to solve this system of linear equations we can use substitution for example:

E = (306.5 -17 V)/18

and use this expression to substitute for E in the second equation:

19  (306.5 - 17 V)/ 18 + 15 V = 298.5

multiplying by 18 on both sides to eliminate denominators, we get:

19 (306.5 - 17 V) + 270 V = 5373

5823.5 - 323 V +270 V = 5373

5823.5 - 53 V = 5373

5823.5 - 5373 = 53 V

450.5 = 53 V

V = 8.5

Therefore the price of the vanilla flavored coffee per pound is $8.50

Now we use this found value in the substitution equation:

E = (306.5 -17 V)/18

E = (306.5 - 17 (8.5))/18

E = 9

Therefore the price of the espresso flavored coffee per pound is $9.00

The pH is the measure of hydrogen ion concentration in a solution. The hydrogen ion concentration at pH 1.25 is  \(5\times 10^{-2}\ M\).

The pH is the negative logarithmic value of the hydrogen ion concentration in the sample.

The pH can be expressed as:

\(\rm pH=-Log[H^+]\)

The hydrogen ion concentration can be given as:

\(\rm [H^+]=10^{-pH}\)

The given pH is 1.25 The hydrogen ion concentration is given as:

\(H^+=10^{-1.25}\\H^+=0.05\ M\\h^+=5\times10^{-2}\ m\)

The hydrogen ion concentration in the solution is .\(5\times 10^{-2}\ M\)

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Answer:

1st blank is 5.62

2nd blank is -2

Step-by-step explanation:

Look at the image (top right corner)

The conclusion made is that at the 2.5% level of significance, there's insufficient evidence to conclude that e-bike ownership and support for building new separated bike lanes are not independent.

The Chi-square test for independence can be used to test the independence between e-bike ownership and support for building new separated bike lanes.

The Null Hypothesis (H0) is that e-bike ownership and support for building new separated bike lanes are independent. The Alternative Hypothesis (H1) is that e-bike ownership and support for building new separated bike lanes are not independent.

Now we can calculate the chi-square statistic:

χ² = ∑ [ (Observed-Expected)² / Expected ]

χ² = 2.439.

For a 2.5% level of significance, the critical value of χ² for 1 degree of freedom is approximately 5.024  which is obtained from a chi-square distribution table.

Because our calculated χ² value is less than the critical value, we do not reject the null hypothesis.

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If we compute a 92% confidence interval in  excel command the critical value will be 1.750686.

Level of confidence c = 0.92

level of significance α = 1 - c = 0.08

A 92% confidence interval has goes from  8/2 = 4% to 100%–(8/2)% = 96%

Leaving 92% in the middle (96%–4%) = 92 %

So look up z-score for 96% or p =0.96

The two closest value in a z-table are

P(z< 1.75) = 0.95994

P(z< 1.76) = 0.96080

Based on this online table

( https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf )

So critical value Z = 1.75 is the closest value , but just barely.

But if you want a more accurate , use the normal function on Excel or from an online calculator or interpolate

If you interpolate

1.75 + (0.96–0.959954)*0.01/ (0.9608–0.95994)

Critical value Z= 1.750535

If you round to four digits,  critical value Z = 1.7505

So the interpolation isn’t that much more accurate

Excel function says critical value Z= 1.750686

=normsinv(0.96)

= 1.750686 which is probably more accurate.

By using the word interval, you have implied you are talking about a two-sided test.

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Answer:

y + 5 = 2(x - 3)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)  

Step-by-step explanation:

Step 1: Define

Point (3, -5)

Slope m = 2

Step 2: Write equation

Substitute in variables into the general form.

y + 5 = 2(x - 3)