The two-way table displays the hair color of the sophomore (So), junior (Jr), and senior (Sr) classes at West Coast High School, represented by percents in the table. A 5-column table has 3 rows. The first column has entries Blonde, brown, total. The second column is labeled Sophomore with entries 10, 10, 20. The third column is labeled Junior with entries 30, 20, 50. The fourth column is labeled Senior with entries 20, 10, 30. The fifth column is labeled Total with entries 60, 40, 100. Let E be the event that the student is blond, and let F be the event that the student is a junior. Are events E and F independent? P(E|F) = % P(E) = % Events E and F are

Answer:

The residual value is the farthest from the line of best fit is 0.7.

Step-by-step explanation:

A simple linear regression line is given by,

[tex]\hat y = \alpha + \beta X + \hat e[/tex]

Here,

α = constant,

β = slope

e = residual.

The difference amid the observed value of the dependent variable (Y) and the predicted value (y) is known as the residual (e).  

The formula to compute the residual is,

[tex]\hat e=y-\hat y[/tex]

The information provided is:

x           y           e

1          2.0       -0.4

2         3.5         0.7

3         5.0        -0.2

4         6.1         -0.6

5         8.0         0.0

The residuals are the difference between the actual value and the predicted value.

They can also be defined as the distance between the line of best fit and the actual value of the dependent variable.

The data point that is the farthest from the line of best fit is, y = 3.5.

The residual value of y = 3.5 is 0.7.

In terms of units distance, this value of y is the farthest from the line of bet fit.

Thus, the residual value is the farthest from the line of best fit is 0.7.

Answer:

  a) 8.7 km

  b) 187.6°

Step-by-step explanation:

Given

Travel vectors (distance)∠(direction) ...

Find

(Rounded to the nearest tenth ...)

  a) |d₂|

  b) ∠d₂

Solution

In order for the sum of the three travel vectors to represent a round trip, their sum must be zero. That is, the value of d₂ must be the opposite of the sum of the other two vectors. A vector calculator can find the desired value easily. Here, we will show the calculation using the law of cosines and the law of sines.

__

a) A diagram can be helpful. Since we want to find the opposite of the sum of the given vectors, we can start by drawing their sum. In our diagram, d₁ is segment AB, and d₃ is segment BC. Their sum is the segment AC.

The internal angle ABC is the supplement of the difference of the angles for d₁ and d₃, so is 180° -(47° -3°) = 136°. Then the law of cosines gives length AC as ...

  AC² = AB² +BC² -2AB·BC·cos(B)

  AC² = 8² +1² -2·8·1·cos(136°) = 65 -16cos(136°) ≈ 76.5094

  AC ≈ √76.5094 ≈ 8.747

The distance traveled on day 2 is about 8.7 km.

__

b) Given the side lengths of a triangle and one angle, the law of sines can be used to find the other angles. Here, it is convenient to find the internal angle at A. The law of sines tells us ...

  sin(A)/BC = sin(B)/AC

  sin(A) = BC/AC·sin(B)

  A = arcsin(BC/AC·sin(B)) = arcsin(1/8.747·sin(136°)) ≈ 4.555°

The direction angle from C to A will be the sum of the 3° direction angle of AB and the internal triangle angle A we just found, added to 180°. That sum is ...

  ∠CA = 180° +3° +4.6° = 187.6°

  ∠d₂ = 187.6°

Answer:

Distance traveled 8.6 kilometers on day two

Daniela traveled in a direcrion of 234degrees on day two

Step-by-step explanation:

I had the same exact question and found the answers after having it incorrect

Answer: 6,3

Step-by-step explanation: 3/3 and then 9/3=3 • 0+12=12, 12/2=6,

Please give brainliest

The system of inequalities consists of x > 6 and x < 3, which have no overlapping solution. No number can satisfy both conditions simultaneously; hence, there is no solution to the system.

To solve the given system of inequalities, let's solve each inequality separately:

For the first inequality 2x - 12 > 0, we add 12 to both sides to get:

2x > 12

Now, we divide both sides by 2:

x > 6

This inequality means that x must be greater than 6.

For the second inequality 3x < 9, we divide both sides by 3:

x < 3

This tells us that x must be less than 3.

If we look at both solutions, x > 6 and x < 3, there is no overlap between these two sets of numbers.

Therefore, there is no solution to the system, since no number can be both greater than 6 and less than 3 at the same time.

Answer:

B

Step-by-step explanation:

English translation:

An employee receives a commission  equivalent to 5% of your salary, X. What

expression represents the total money that  will receive the employee?

Solution:

We have to find the expression that gives us the total money of the employee. His total money is what he gets, the salary, PLUS the commissions.

His salary is "x"

and his commissions is 5% of his salary.

5% = 5/100 = 0.05

So,

Commissions = 0.05x

Total Money = Salary + Commission = x + 0.05x = 1.05x

Correct answer is B

Answer:

24.25 units for a.pe.x if the triangle has the sides x,14, and 28

Step-by-step explanation:

The value of the labeled side , x is 24.25 units.

From pythagoras :

From the question given:

Now we have ;

Adjacent = √(784 - 196)

Adjacent = √588

Adjacent = 24.248

Hence, the value of x = 24.25 units.

Learn more on Pythagoras: https://brainly.com/question/231802

#SPJ2

Answer:

525 people

Step-by-step explanation:

3000/200=15

You multiply 15 by 35

This equals 525.

Answer:

525

Step-by-step explanation:

heres why

because 35/200 is a fraction that can be used in decimal form to multipy with 3000 to find the total ammount of people that said that this was their first concert

the decimal used is .175 so multply that with 3000 and you get 525

If brainiest is earned its greatly Appreciated

Answer:

a

Step-by-step explanation:

Check out the diagram below. Note how for the left triangle, the side ZW is not between the marked angles V and W. So we do not use ASA and instead go with AAS. The order matters. If for instance, we knew that VW = WY, then we would go with ASA.

Answer:

s = -18

b is correct option

Step-by-step explanation:

[tex]\frac{4}{s} =\frac{-2}{9}[/tex]

By cross multiplication

4×9 = -2×s

0r

-2×s = 4×9

s = 36 ÷ -2

s = -18

Answer:

The answer is D

Step-by-step explanation:

The solution set of {x | x > -5} u {x | x < 5} is given by all real numbers. so option D is correct.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality. A set of such values is called a solution set to the considered equation or inequality.

We need to find the solution set of the following inequalities:

A set of {x | x > -5} u {x | x < 5} has the solution of all values of x greater than -5.

The solution is all values of x greater than -5.

This is the union of both the inequalities, therefore all the real numbers will justify the inequalities.

Then, the solution set of {x | x > -5} u {x | x < 5} is given by all real numbers. so option D is correct.

Learn more about inequalities here:

https://brainly.com/question/27425770

#SPJ2

Answer:

x=23

Step-by-step explanation:

180-145= 35 so you have to set the equation to 35. 3x-34=35. add 34 to each side. now you have 3x=69. divide 3 on each side and you get x=23

Answer:

95%

Step-by-step explanation:

Let the proportion who can swim be denoted by P(S) while the proportion that can whistle be denoted by P(W)

The proportion that can swim and whistle will be P(S and W)

The proportion that can swim or whistle will be P(S or W)

To get the proportion that can swim or whistle will be P(S or W), we use

P(S or W)=P(S)+P(W)-P(S and W)

Given that P(W) is 70%, P(S) is 80% and P(S andW) is 55% then

P(S or W)=80%+70%-55%=95%

Answer:

7/12.

Step-by-step explanation:

The total possible outcomes = 6*6 = 36.

Possible outcomes for a total  8 or greater are :

2,6  6,2  3,5   5,3  3,6  6,3   4,4  4,5  5,4  4,6  6,4  5,5,  5,6  6,5  6,6 = 15.

So the number of outcomes for a sum < 8 = 36 - 15 = 21.

Answer is 21/36 = 7/12.

The volume of a cylinder is the area of the base circle times the height.

The area of a circle is [tex]\pi r^2[/tex]. Since the diameter is 19.05, the radius will be half that diameter:

[tex]r=\dfrac{d}{2}=\dfrac{19.05}{2}=9.525[/tex]

So, the base area is

[tex]A=\pi(9.525)^2[/tex]

Multiply this by the thickness and you'll get the volume.

Final answer:

The approximate volume of a roll of pennies can be calculated using the volume formula for a cylinder, considering the diameter and thickness of a penny, converting measurements to the same units, and then multiplying by the number of pennies in a roll.

Explanation:

To solve for the approximate volume of a roll of pennies, we can use the formula for the volume of a cylinder, which is V = πr^2h, where r is the radius and h is the height of the cylinder. In this case, the diameter of a penny is given as 19.05 mm, which means the radius is half of that, 9.525 mm or 0.9525 cm. The thickness of each penny is 1.52 mm or 0.152 cm. If we assume a roll of 50 pennies, the height of the roll would be 50 times the thickness of one penny.

First, we convert the radius into centimeters by dividing by 10: 0.9525 cm. Then we use the formula to calculate the volume: V = π * (0.9525 cm)^2 * (0.152 cm * 50), which provides the volume of the roll of pennies. As the question asks to approximate the volume to the nearest tenth, we can perform this calculation and round the result accordingly.

Volume calculation and unit conversion are crucial elements in this type of problem. Moreover, the accuracy of the estimation is important, which should be within an acceptable range like 5%.

April has a total of 6 pieces of paper, with each piece being 4 inches long after she cuts the 2-foot paper into halves and then into thirds.

To solve this problem, we need to perform two cuts. The initial length of the paper is 2 feet. When April cuts the length of paper into halves, she now has two pieces each of 1 foot in length. Then, she cuts each of these halves into thirds. To find out how many pieces she has in total, we multiply 2 halves by 3, resulting in 6 pieces of paper in total.

To determine the length of each piece in inches, we start with the original measurement in feet. Since 1 foot is equivalent to 12 inches, we convert the 1-foot pieces to inches by multiplying by 12. Then, we divide by 3 to represent the three cuts that April makes:

1 foot = 12 inches

Each cut piece = 12 inches / 3

Each piece is 4 inches long.

Answer:

Step-by-step explanation:

To the evaluate -5.3+7.9

We get

2.6

Therefore the error

=2.6-2.4

=0.2

When we graph the function, it has a vertex of (3, 16).

The maximum of the graph is the highest "x" value on the graph which is 3.

Since the maximum is 3, it will take 3 seconds for the ball to reach its maximum height.

A graph will be shown below showing the function and vertex.

Best of Luck!

Answer:

3 seconds

Step-by-step explanation:

We need to find where the maximum i.  The maximum or minimum  is at the vertex.  We know where the zero are because the equation is written in the zero form

We know the vertex is 1/2 way between the zeros

h(x)=-(x+1)(x-7)

Using the zero product property

x+1 = 0  x-7 =0

The zeros are at -1 and 7

Adding the two together and dividing by 2

(-1+7)/2 = 6/2 =3

The maximum is at 3.  We know it is the maximum because the equation is pointing down because of the negative out front.

Answer: yes her calculations were reasonable because : 63/12=5.25

Step-by-step explanation:

Final answer:

Heather's estimation that each light costs about $5 is closer to the actual cost of $5.25 per light. Her calculated cost of $2.40 per light is not reasonable as it significantly underestimates the actual cost.

Explanation:

The question is asking whether Heather's calculation for the actual cost of each patio light is reasonable. Initially, Heather estimated each light to cost about $5, but after calculation, she found the cost to be $2.40. To verify this, we can divide the total cost by the number of lights. So, the calculation is as follows:

Total cost for 12 lights = $63

Actual cost per light = Total cost / Number of lights

Actual cost per light = $63 / 12

Actual cost per light = $5.25

Based on this calculation, Heather's estimate of $5 per light was closer to the actual cost, which is $5.25 per light. Therefore, her calculation of $2.40 per light is not reasonable as it is quite far from the actual calculated cost.

Answer:

1. 130/6

2. 65/3

3. 260/12

Step-by-step explanation:

The first thing is to calculate the weight of 10 quarts of milk, like this:

(13 pounds / 6 quarts) * 10 quarts = 130/6 pounds

The three fractions could be:

1. 130/6 pounds weigh 10 quarts of milk.

2. 65/3 pounds weigh 10 quarts of milk.

3. 260/12 pounds weigh 10 quarts of milk.

Answer:

[tex]5 {y}^{2} (4 {y}^{4} - 3 {y}^{2} + 8)[/tex]

Step-by-step explanation:

We want to factor the common monomial out of :

[tex]20 {y}^{6} - 15 {y}^{4} + 40 {y}^{2} [/tex]

The greatest common monomial fact is

[tex]5 {y}^{2} [/tex]

We factor to get:

[tex]5 {y}^{2} (4 {y}^{4} - 3 {y}^{2} + 8)[/tex]

The expression in the parenthesis has no common factor again since we factored the greatest common factor.

The greatest common factor of 20y^620y

6

20, y, start superscript, 6, end superscript, -15y^4−15y

4

minus, 15, y, start superscript, 4, end superscript, and 40y^240y

2

40, y, squared is 5y^25y

2

5, y, squared.

[Show me how to find the greatest common factor.]

Now we need to factor 5y^25y

2

5, y, squared out of 20y^6-15y^4+40y^220y

6

−15y

4

+40y

2

20, y, start superscript, 6, end superscript, minus, 15, y, start superscript, 4, end superscript, plus, 40, y, squared.

Hint #22 / 3

\begin{aligned} &\phantom{=}20y^6-15y^4+40y^2 \\\\ &=5y^2(4y^4)+5y^2(-3y^2)+5y^2(8) \\\\ &=5y^2\left(4y^4-3y^2+8\right) \end{aligned}

​

=20y

6

−15y

4

+40y

2

=5y

2

(4y

4

)+5y

2

(−3y

2

)+5y

2

(8)

=5y

2

(4y

4

−3y

2

+8)

​

Hint #33 / 3

In conclusion,

20y^6-15y^4+40y^2=5y^2\left(4y^4-3y^2+8\right)20y

6

−15y

4

+40y

2

=5y

2

(4y

4

−3y

2

+8)20, y, start superscript, 6, end superscript, minus, 15, y, start superscript, 4, end superscript, plus, 40, y, squared, equals, 5, y, squared, left parenthesis, 4, y, start superscript, 4, end superscript, minus, 3, y, squared, plus, 8, right parenthesis

Answer:

I believe the answer is A

Answer:

907.46cm

Step-by-step explanation:

Area of Cirlce = πr^2

R= 17

R^2= 289

289 x 3.14 = 907.46

907.46cm

Answer:

Area of the circle = [tex]907.46\;cm^2[/tex]

Step-by-step explanation:

Diameter of the DVD = [tex]34\;cm[/tex]

[tex]Radius=\dfrac{34}{2}=17\;cm[/tex]

Area of the circle= [tex]\pi \times r^2[/tex]

      As,

         [tex]\pi =\dfrac{22}{7}=3.14[/tex]

Area is:

      [tex]=3.14\times 17\times 17\\\\=3.14\times 289\\\\=907.46\;cm^2[/tex]

Area of the circle is: [tex]907.46\;cm^2[/tex]

Answer:

The answer is about 1.732, the exact form being [tex]\sqrt{3}[/tex].

Step-by-step explanation:

The square root of 12 is 3.4641. You then divide this by 2 and you get approximately 1.732. This in the exact form is [tex]\sqrt{3}[/tex].

Answer:y=-2x+3

Step-by-step explanation:

the 3 is the y coordinate

the slope is -2

Answer: 165 bags

Step-by-step explanation:

Final answer:

The binomials that are a difference of squares are [tex]9x^2 - 16[/tex] and [tex]m^6 - 25[/tex], as both can be factored into the form (a + b)(a - b).

Explanation:

The question asks which binomials are a difference of squares. A difference of squares is a binomial in the form [tex]a^2 - b^2[/tex], which can be factored into (a + b)(a - b). Analyzing the given options:

[tex]y^4 + 9[/tex]: This is not a difference, it's a sum.

[tex]9x^2 - 16[/tex]: This is a difference of squares because [tex]9x^2 = (3x)^2[/tex] and 16 = [tex]4^2[/tex].

[tex]m^6 - 25[/tex]: This is a difference of squares because [tex]m^6 = (m3)^2[/tex] and [tex]25 = 5^2[/tex].

[tex]p^7 - 1[/tex]: This is not a difference of perfect squares; [tex]p^7[/tex] is not a perfect square.

Therefore, the binomials that are a difference of squares are [tex]9x^2 - 16[/tex] and [tex]m^6 - 25[/tex].

Answer:

y = 6/5x -5

Step-by-step explanation:

Using the slope formula,

you can find the slope

or just divide the amount of units up by

the amount of units right.

Then find the y intercept which is (0,5)

Answer:

y = [tex]\frac{6}{5}[/tex]x -5

Step-by-step explanation:

Whenever we have a line such as this one, (A linear or straight line) we can write an equation with the form y = mx + b

m is the slope

b is the y-intercept

To calculate slope or "m" we see how many times the point goes up, and how many times it goes to the right, and then put it in a fraction.

(Units it goes up) / (Units it goes to the right)

The y-intercept is what number the line intersects on the y-axis.

On this line it intersects at the -5 point.

So the equation when you put in the values is y = [tex]\frac{6}{5}[/tex]x -5

Probability of choosing pink balloon is  [tex]\frac{2}{5}[/tex].

Step-by-step explanation:

Given,

Number of green balloons = 5

Number of yellow balloons = 3

Number of red balloons = 4

Number of pink balloons = 8

Total number of balloons = 5+3+4+8 = 20

To find the probability of pink balloon.

Formula

Probability of an even = number of outcomes ÷ total number of outcomes

So,

Probability of choosing pink balloon = [tex]\frac{8}{20}[/tex] = [tex]\frac{2}{5}[/tex]