Let event A = You buy a new umbrella on Friday. Which event is most likely to
be independent of A?

Answer:

3/6 or 50%

Step-by-step explanation:

The probability of rolling an odd number from the dice numbered,  {1,2,3,4,5,6} is 3/6.

6 numbers in all.

3 odd numbers.

3 even numbers.

Therefore, 3/6 or 50%.

Answer:

Part 6) Option B $3.20

Part 7) Option C. 8,295 students

Step-by-step explanation:

Part 6)

Let

x -----> the cost of one hamburger

y ----> the cost of one soda

we know that

7x+3y=27.95 ------> equation A

5x+4y=23.40 ----> equation B

Solve the system by graphing

Remember that the solution by graphing is the intersection point both graphs

using a graphing tool

The solution is the point (3.2,1.85)

see the attached figure N 1

therefore

The cost of one hamburger is $3.20

Part 7)

Let

x -----> the number of students

y -----> the number of teachers

we know that

x=35y ------> equation A

x+y=8,544-12

x+y=8,532 -----> equation B

Solve the system by substitution

substitute equation A in equation B and solve for y

35y+y=8,532

36y=8,532

y=237 teachers

Find the value of x

x=35y ------> x=35(237)=8,295

therefore

The number of students is 8,295

Step-by-step explanation:

solve the equation:

5x-10=4x+20

Answer:

The correct answer is option B. 140

Step-by-step explanation:

From the figure we can see that,

AB ║ CD

To find the value of x

From the figure we can see that,

<CFE = <BEF      [Alternate interior angles are equal]

4x + 20 = 5x - 10

5x - 4x = 20 + 10

x = 30

To find the measure of <BEF

m<BEF = 5x - 10

 = (5*30) - 10

 = 150 - 10

 = 140°

Therefore the correct answer is option B. 140

To find the value of x, we set the expressions for the sides of the rectangle equal to each other (4x - 16 = x + 5) and solve for x to get x = 7.

The student has asked to find the value of x given that QRST is a rectangle with sides RT and SQ. Since in a rectangle opposite sides are equal, we can set the expressions for RT and SQ equal to each other:

RT = SQ

4x – 16 = x + 5

To solve for x, we must do some algebra. Subtract x from both sides of the equation:

4x – x – 16 = 5

Combine like terms:

3x – 16 = 5

Add 16 to both sides:

3x = 21

Divide by 3:

x = 7

Therefore, the value of x is 7.

Answer:

Perpendicular

Step-by-step explanation:

Definition of perpendicular lines:

Lines that intersect forming a right angle are perpendicular lines.

Answer:

Perpendicular

Step-by-step explanation:

Answer:

the line of best feet passes through three poin

Step-by-step explanation:

1st three points are green, yellow and red

2nd three point are green yellow and upward green

Final answer:

The outlier with a large residual indicates it does not fit the line of best fit, and removing it can improve the model's accuracy. After recalculating without the outlier, a stronger correlation coefficient of 0.9121 suggests that the line of best fit models the data better.

Explanation:

Understanding Residuals and Outliers in Linear Regression

In the context of linear regression, a residual is the difference between the observed value of the dependent variable (y) and the predicted value (ý) provided by the regression model. We are testing the residuals to determine how closely the regression line models the actual data points. If a residual is larger than twice the standard deviation (in this case, greater than 32.8 or less than -32.8), the corresponding data point is considered an outlier. The single large outlier identified with a grade of 65 on the third exam and 175 on the final exam has a substantial residual of 35, indicating that this data point does not fit well with the line of best fit. This outlier can significantly affect the regression line's slope and y-intercept.

Outliers can have a significant impact on the best-fit line, potentially skewing the results and affecting predictions. To assess the outlier's influence, we can remove it and re-calculate the best-fit line and correlation coefficient. If the coefficient is closer to 1 or -1 and the sum of squared errors (SSE) is lower after re-calculating, this indicates a better fit. In this case, the line of best fit without the outlier provides a correlation coefficient of 0.9121, suggesting a stronger linear relationship between the third exam and final exam scores after removing the outlier.

Answer:

2)A plane has length and width.

3)A plane extends infinitely in all directions

5)A plane is a flat surface.

Step-by-step explanation:

We can think of a plane as a line in space with no height, only length and width.

Yes, a plane is a two-dimensional surface, hence it has length and width.

2)A plane has length and width (TRUE)

The plane surface extends infinitely far, therefore it extends infinitely in all direction.

3)A plane extends infinitely in all directions (TRUE)

5)A plane is a flat surface(TRUE)

The correct options are 2,3 and 5.

See attachment

Answer:

B,C,E

Step-by-step explanation:

Answer:

B about $98,000

Step-by-step explanation:

The equation that models the sales of the product after an initial release is:

[tex]S = 16 \sqrt{3t} + 25[/tex]

where s represents the total sales (in thousands) and t represents

the time in weeks after release.

The table and graph is shown in the attachment.

From the graph we estimate the sales

7 weeks after release to be about 98 thousands dollars.

The correct choice is B.

Answer:

Option C. The system of the equations has no solution; the two lines are parallel.

Step-by-step explanation:

we have

-3x+4y=12 -----> equation A

(1/4)x-(1/3)y=1 ----> equation B

Multiply equation B by -12 both sides

-12*[(1/4)x-(1/3)y]=1*(-12)

-3x+4y=-12 ----> equation C

Compare equation A and equation C

The lines are parallel , but the y-intercepts are different

therefore

The system has no solution

Answer:

[tex]\frac{60c}{m}[/tex]

Step-by-step explanation:

We can use the unity rule to solve this problem.

Number of toys made in m minutes = c

Number of toys made in 1 minute = [tex]\frac{c}{m}[/tex]

Number of toys made in 60 minutes = [tex]\frac{c}{m} \times 60 = \frac{60c}{m}[/tex]

Since 60 minutes = 1 hours, we can write:

Number of toys made in 1 hour = [tex]\frac{60c}{m}[/tex]

Therefore, we can say that Kevin makes [tex]\frac{60c}{m}[/tex] toys per an hour.

Answer:

y = 2x - 5

Step-by-step explanation:

We are to find the equation of line the line which passes through the points (4, 3) and (2, -1).

Finding the slope:

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

Substituting the coordinates of one of the given points and slope in the standard form of an equation to find the y intercept.

[tex]y=mx+c[/tex]

[tex] -1 = 2 (2) + c \\\\ c = - 5 [/tex]

So the equation of the line would be [tex]y=2x-5[/tex]

Answer: first option.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

To find "m", we need to substitute the coordinates of the points  (4, 3) and (2, -1) into this formula:

 [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

We can identify that:

[tex]y_2=-1\\y_1=3\\x_2=2\\x_1=4[/tex]

Then:

[tex]m=\frac{-1-3}{2-4}\\\\m=2[/tex]

To find "b" we must substitute the slope and one of the given points into [tex]y=mx+b[/tex] and solve for "b". Then, this is:

[tex]3=2(4)+b\\\\3-8=b\\\\b=-5[/tex]

Therefore, the equation of this line is:

[tex]y=2x-5[/tex]

Final answer:

The volume of the oblique rectangular prism is calculated using the length, width, and height. The formula V = l  times w  times h gives a volume of 504 cubic centimeters.

Explanation:

To find the volume of an oblique rectangular prism, we use the same formula as for a right rectangular prism because the volume is not affected by the obliquity of the sides. The formula for the volume (V) is the product of the length (l), width (w), and height (h). So, using the provided dimensions:

V =l  times w  times h = 8 cm  times 7 cm times 9 c

Now, let's calculate:

V = 8  times 7  times 9 = 504 cm

Therefore, the volume of the oblique rectangular prism is 504 cubic centimeters.

Answer:

A' = (6 , 10) , B' = (4 , 7) , C' = (1 , 7) , D' = (1 , 11) , E' = (2 , 12)

Step-by-step explanation:

* Lets revise the rotation and translation

- If point (x , y) rotated about the origin by angle 90° counterclockwise

 ∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 180° counterclockwise

 ∴ Its image is (-x , -y)

- If point (x , y) rotated about the origin by angle 270° counterclockwise

 ∴ Its image is (y , -x)

- If the point (x , y) translated horizontally to the right by h units

 ∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 ∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

 ∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

 ∴ Its image is (x , y - k)

* Now lets solve the problem

- The vertices of the polygon are:

  A = (-7 , 8) , (B = (-4 , 6) , C = (-4 , 3) , D = (-8 , 3) , E = (-9 , 6)

- The polygon rotates 270° counterclockwise about the origin

∵ Point (x , y) rotated about the origin by angle 270° counterclockwise

∴ Its image is (y , -x)

∵ A = (-7 , 8)

∴ Its image = (8 , 7)

∵ B = (-4 , 6)

∴ Its image = (6 , 4)

∵ C = (-4 , 3)

∴ Its image = (3 , 4)

∵ D = (-8 , 3)

∴ Its image = (3 , 8)

∵ E = (-9 , 6)

∴ Its image = (6 , 9)

- After the rotation the image will translate 2 units to the left and

 3 units up

∴ We will subtract 2 units from each x-coordinates of the vertices and

  add 3 units to each y-coordinates of the vertices

∵ Point (x , y) translated horizontally to the left by h units

∴ Its image is (x - h , y)

∵ Point (x , y) translated vertically up by k units

∴ Its image is (x , y + k)

∴ A' = (8 - 2 , 7 + 3)

∴ A' = (6 , 10)

∴ B' = (6 - 2 , 4 + 3)

∴ B' = (4 , 7)

∴ C' = (3 - 2 , 4 + 3)

∴ C' = (1 , 7)

∴ D' = (3 - 2 , 8 + 3)

∴ D' = (1 , 11)

∴ E' = (6 - 2 , 9 + 3)

∴ E' = (4 , 12)

* The coordinates of its image are:

  A' = (6 , 10) , B' = (4 , 7) , C' = (1 , 7) , D' = (1 , 11) , E' = (2 , 12)

After a 270° counterclockwise rotation and 2 units left and 3 units up translations, the polygon's image has the new coordinates A''(-10,-4), B''(-8,-1), C''(-5,-1), D''(-5,-5), and E''(-8, -6).

In trigonometry and geometry, a 270° counterclockwise rotation of a point (x, y) about the origin gives a new point (-y, x). Now, let us consider the transformation of point A(-7, 8). After a 270° rotation, the new point is A'(-8, -7) and after translating 2 units left and 3 units up, the final transformed point A'' is (-8-2, -7+3) = (-10, -4).

Following the same process, B'(-6, -4), C'(-3, -4), D'(-3, -8), E'(-6, -9) and, after translation, B''(-8, -1), C''(-5, -1), D''(-5, -5), E''(-8, -6). Thus, the coordinates of the polygon A'B'C'D'E' after a 270° counterclockwise rotation and a 2 unit left and 3 units up translations are A''(-10,-4), B''(-8,-1), C''(-5,-1), D''(-5,-5), and E''(-8, -6).

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Answer:

445 dollars

Step-by-step explanation:

You are given he charges 47.5 per hour so 47.5x is how much you will pay for x hours and he charges a 65 dollar service fee.

So together he is charge you 47.5x+65 for x hours.

If it spends 8 hours, the cost will be 47.5(8)+65=445.

The total charges if it takes the plumber 8hours to complete the task is $445.00

According to the question,

For 1 hour the charge is $47.50

∴ For 8 hours, the charge is $(47.50 x 8) = $ 380

The service charge is to be added now.

∴ The final amount of money = $(380.00 + 65.00) = $445.00

The total charge is $ 445.00

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Answer:

-7/5 if your function really is f(x)=-5x-7

Step-by-step explanation:

The zeros of an expression are the numbers you can plug into that expression that will make that expression 0.

So what value of x will make the expression

-5x-7=0.

You don't have to this by observation. We can just solve it and see.

-5x-7=0

Add 7 on both sides:

-5x. =7

Divide both sides by -5:

x. =7/-5

x. =-7/5

So -7/5 will make the expression equal to 0.

Let's test this:

-5x-7 when x=-7/5

-5(-7/5)-7

7-7

0

So it does indeed.

Answer:

Step-by-step explanation:

The polynomial y = (x + 4)(x - 2)(x + 7) has 3 roots.

y = 0 ⇒ (x + 4)(x - 2)(x + 7) = 0 ⇔ x + 4 = 0 ∨ x - 2 = 0 ∨ x + 7 = 0

x + 4 = 0   subtract 4 from both sides

x = -4

x - 2 = 0      add 2 to both sides

x = 2

x + 7 = 0      subtract 7 from both sides

x = -7

The polynomial function y = (x + 4)(x - 2)(x + 7) has three distinct roots: -4, 2, and -7.A. 3

The polynomial function y = (x + 4)(x - 2)(x + 7) has three distinct roots, which can be found by setting y to zero and solving for the values of x that make the function equal to zero. When you set y to zero, the equation becomes 0 = (x + 4)(x - 2)(x + 7), and the roots are x = -4, x = 2, and x = -7. Hence, the correct answer to the question of how many roots the polynomial function has is:

A. 3

Answer:

O D. (2,5)

Step-by-step explanation:

y > 2x - 3

Substitute the points into the inequality and see if it is true

(3,2)

2 > 2(3) - 3

2> 6-3

2>3  False

(9,12)

12 > 2(9) - 3

12> 18-3

12>15  False

(4,4)

4 > 2(4) - 3

4> 8-3

4>5  False

(2,5)

5 > 2(2) - 3

5> 4-3

5>1  True

Answer:D

Step-by-step explanation:

Answer:

Im pretty sure its C

Step-by-step explanation:

because when u line up the the right angles u see the hypotenuse and leg of another triangle is the same

The given triangles are not congruent since the hypotenuse of one triangle is equal to the length of leg of another triangle.

So the corresponding sides of the triangles are not equal.

So the triangles are not congruent.

So, option C is correct.

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Answer:

m∠B = 90°

Step-by-step explanation:

Note that the figure given to you is a triangle, which has 3 angles, and the total measurement of 3 angles is = 180°.

Let m∠B = x

     m∠A = 60°

     m∠C = 30°

Set the equation:

m∠A + m∠B + m∠C = 180°

Plug in the corresponding numbers to the corresponding variables:

60 + x + 30 = 180

Isolate the variable, x. Combine like terms:

x + (60 + 30) = 180

x + (90) = 180

Isolate the variable, x. Subtract 90 from both sides:

x + 90 (-90) = 180 (-90)

x = 180 - 90

x = 90

m∠B = 90°

Answer:

C'D'=3 units

Step-by-step explanation:

we know that

The translation of a segment does not modify its length

so

The length of the segment CD and the length of the segment C'D' are equal

therefore

C'D'=3 units

Verify

Let

The coordinate of point C equal to x1 and the coordinate of point D equal to x2

so

The length of segment CD is equal to

CD=x2-x1=3

The rule of the translation is

x ------> x+2

The new coordinates will be

C'=x1+2

D'=x2+2

The length of segment C'D' is equal to

(x2+2)-(x1+2)=(x2-x1)=3 units

Answer:

D 3

Step-by-step explanation:

Answer:

remain the same, may change

Step-by-step explanation:

When a figure is rotated, its angle measured remains the same and its orientation remains the same.

The circular movement of an object around a rotation axis is known as rotation. An infinite number of rotation axes can exist in a three-dimensional object.

Therefore When a figure is rotated, its angle measured remains the same and its orientation remains the same.

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Answer: C: 3rd degree polynomial wit 3 terms.

Step-by-step explanation: The polynomial has 3 terms and the highest degree is 3.

C. Third degree polynomial with three terms.

Terms are, by definition, the number of nonzero coefficients for powers of x. In this case, there are 3 nonzero coefficients (3 terms) because [tex]-1=-1x^0[/tex]. For example, [tex]2x^3[/tex] has one term, but [tex]0[/tex] has 0 terms.

The degree of a polynomial is the highest power involved in the expression. In this case, it's [tex]4x^3[/tex], so the degree is 3.

Answer:

Part 1) The library is located at point (3.25,-1.5)

Part 2) The library is 1.5 miles from Road X

Part 3) The library is 3.25 miles from Road Y

Step-by-step explanation:

step 1

Find the coordinates of the library

we know that

Observing the graph

The length of each square in the graph is 0.5 miles

so

The coordinates of point L are (3.25,-1.5)

therefore

The library is located at point (3.25,-1.5)

step 2

Find the distance of the library from road X

we know that

The distance of point L from road X is the perpendicular distance of point L to the Road X

The perpendicular distance is the absolute value of the y-coordinate of point L

therefore

The library is 1.5 miles from Road X

step 3

Find the distance of the library from road Y

we know that

The distance of point L from road Y is the perpendicular distance of point L to the Road Y

The perpendicular distance is the absolute value of the x-coordinate of point L

therefore

The library is 3.25 miles from Road Y

Answer:

[tex]5\sqrt{5}[/tex]

Step-by-step explanation:

We start by factoring 125 and look for a perfect square:

125= 5*5*5=[tex]5^{2} *5[/tex].

This allow us to simplify the radical:

[tex]\sqrt{125} = \sqrt{5^{2} *5}[/tex]

So we have:

[tex]\sqrt{5^{2} *5} =5\sqrt{5}[/tex]

Answer:

172°

Step-by-step explanation:

Connect the center of the circle with two endpoints of the chord. You'll get the isosceles triangle with the angles adjacent to the base of

[tex]94^{\circ}-90^{\circ}=4^{\circ}[/tex]

Then the angle between two congruent sided (two radii of the circle) is

[tex]180^{\circ}-2\cdot 4^{\circ}=172^{\circ}[/tex]

This angle is central angle subtended on the arc z, so the measure of z is 172°.

Answer: OPTION B.

Step-by-step explanation:

It is important to remember that:

[tex]Tangent\ chord\ angle=\frac{1}{2}(Intercepted\ arc)[/tex]

We can identify in the figure that 94° is the measure of a tangent chord angle. Then, we can find "x":

[tex]94\°=\frac{1}{2}x\\\\(2)(94\°)=x\\\\x=188\°[/tex]

Since there are 360° in a circle, we can subtract 360° and the value of "x" to find the value of "z". Then we get:

[tex]z=360\°-x\\\\z=360\°-188\°\\\\z=172\°[/tex]

Answer:

Option 1: {x | x > 12 or x < 6}

Step-by-step explanation:

Given inequalities will be solved one by one:

[tex]\frac{2}{3}x >8\\2x > 8*3\\2x>24\\x > \frac{24}{12} \\x>12[/tex]

Or

[tex]\frac{2}{3}x<4\\2x<4*3\\2x<12\\x < \frac{12}{2}\\ x<6[/tex]

Hence we can see that the solution of both inequalities combined is:

x>12 or x<6

Hence, option 1 is correct ..

Answer:

1/2 hr.

Step-by-step explanation:

Make a whole number of the wall. In this case, multiply by 2:

1/2 x 2 = 2

Because you multiplied 2 to the wall, you must also multiply 2 to the hours:

1/4 x 2 = 2/4

Remember to simplify:

(2/4)/(2/2) = 1/2

It will take you 1/2 hr to paint one wall.

~

30 minutes

A quarter of an hour is 15 minutes, because 60÷4=15.

So, this means that half of a wall equals to 15 minutes.

If you painted half of a wall, you have another half remaining.

Therefore, 2×15=30

30 minutes is the answere

Answer:

constant of variation = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 2 when x = 4

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

The constant of variation is 1/2.

Step-by-step explanation:

y = kx where k is the constant of variation.

So k = y/x = 2/4 = 1/2.