Put these numbers in order from greatest to least.
-24/40
0.5
66 6/15
66.2
-0.4

Let the speed of the small plane be 'R'.

Let the speed of the wind be 'S'.

Plane's time against wind = 2 hours and 10 minutes  = 13/6 hours.

Plane's time with wind = 1 hour and 50 minutes = 11/6 hours

Use formula;

Distance =  speed x time

Against the wind:

858 = (13/6) (R-S)  = (13/6) R - (13/6)S

With wind:

858 = (11/6)(R + S) = (11/6)R + (11/6)S  

Multiplies each by 6.

5148 = 13R - 13S

5148 = 11R + 11S

Use elimination method

56628 = 143R - 143S  (multiplies by 11)

66924 = 143R + 143S  (multiplies by 13)

Further solving;

123552 = 276R

R = 432 miles/ hr. (speed of small plane )

And,  S = 36 miles/ hr. (speed of wind)

To know more about the speed and time, here

https://brainly.com/question/13262646

#SPJ4

The solutions of the given quadratic equation are

[tex]x = 3 \ or \ x = -\frac{1}{4}[/tex]

What is quadratic equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A two degree equation is known as Quadratic equation.

The given quadratic equation is

[tex]4x^2 - 11x - 3[/tex]

Now,

[tex]4x^2 - 11x - 3 = 0\\\\(2x)^2 - 2 \times 2x \times \frac{11}{4} + (\frac{11}{4})^2 - (\frac{11}{4})^2 -3 = 0\\\\(2x - \frac{11}{4})^2 = \frac{121}{16} + 3\\\\(2x - \frac{11}{4})^2 = \frac{121+48}{16}\\\\(2x - \frac{11}{4})^2 = \frac{169}{16}\\\\2x - \frac{11}{4} = \sqrt{\frac{169}{16}}\\\\2x - \frac{11}{4} = \pm\frac{13}{4}\\\\2x - \frac{11}{4} = \frac{13}{4} \ or \ 2x - \frac{11}{4} = -\frac{13}{4}\\\\2x = \frac{13}{4} + \frac{11}{4} \ or \ 2x = \frac{11}{4} - \frac{13}{4}\\\\[/tex]

[tex]2x = 6 \ or \ 2x = -\frac{1}{2}\\x = 3 \ or \ x = -\frac{1}{4}[/tex]

To learn more about quadratic equation, refer to the link-

https://brainly.com/question/25841119

#SPJ1

Based on this if we find the 10% of the population we have:

15000000 × 0.1 = 1500000 And we see that our sample 1600 & lt;

1500000 and we satisfy the 10% condition.

For this case we have the following data given:

n = 1600 represent the sample size select.

dp = 0.43, which,  represent the estimated proportion of high school students that have a part time job

N= 15000000 represent the total population size

And we want to check if the 10% condition is satisfied. So we can use the following definitions for the 10% condition: “We need to have Bernoulli trials must be independent.

If that assumption is not satisfied, it is  still okay to proceed if we have that the sample is smaller than 10% of the population.”"One of the conditions to be checked before using the normal model for sample proportions is, “The sample size, n, must be no larger than 10% of the population.

”So based on this if we find the 10% of the population we have:

15000000 × 0.1 = 1500000

And we see that our sample 1600 & lt;

1500000 and we satisfy the 10% condition.

Learn more about Percentage:

https://brainly.com/question/24120406

#SPJ4

The expression, (–5.5 + 2p)(–2), after simplification is 11-4p.

According to the question,

We have the following expression:

(–5.5 + 2p)(–2)

Now, in order to simplify this expression, we will multiply -2 into the bracket:

(Note that when a number or a variable is multiplied into the bracket then it is multiplied into every number or term within the bracket.)

-5.5*-2+2p*(-2)

We know that when two negative integers are multiplied then the result is positive and when one negative and one positive integer is multiplied then the result is negative.

11-4p

Hence, the expression, (–5.5 + 2p)(–2), after simplification is 11-4p.

To know more about expression here

https://brainly.com/question/14083225

#SPJ1

Answer:

x = 12

Step-by-step explanation: You start off with this

3x + 2

Then since AC is 38 you make it

3x+2=38

Then you do -2 getting rid of the 2 and doing 38 - 2 which is 36

you now have:

3x = 36

then you do 3x divided by 3 on both sides

you do 36 divided by 3 then you get

x = 12

Both the pairs of the points are linear.

Here i made the plot for the points and both the pairs of the points shows that the it follows a straight path which means it will be linear i nature.

To know more about linear. https://brainly.com/question/2541253

#SPJ1

The measure of each exterior angles of a regular hexagon is 60  degrees

The interior angle of the regular polygon is

d = 180(n - 2) / n

Where d is the measure of interior angle

n is the number of sides

The number of sides in a regular hexagon

d = 180(6 - 2) / 6

= 180×4 / 6

= 720 / 6

=120 degrees

The each interior angle of the regular hexagon is 120 degrees

The measure of exterior angle = 180 - The measure of interior angle

= 180 - 120

= 60 degrees

Hence, the measure of each exterior angles of a regular hexagon is 60  degrees

Learn more about hexagon here

brainly.com/question/13293407

#SPJ1

5. Based on arc and central angle relationship, m∠BCD is: B. 108°.

6. The length of arc PQ is: H. 3.14 m

7. Length of CF is: A. 6 cm.

To find the length of an arc, the formula to use is:

Arc length = ∅/360 × 2πr

5. Measure of arc AB = 72°

Measure of arc BD = 180 - measure of arc AB

Measure of arc BD = 180 - 72

Measure of arc BD = 108°

Measure of angle BCD = measure of arc BD [central angle theorem]

Measure of angle BCD = 108°

The answer is: B. 108°

6. ∅ = 60°

r = 3 m

Arc length = 60/360 × 2 × π × 3

Arc length = 3.14 m

The answer is: H. 3.14 m

7. Since the distance between the two chords, AB and CD are equal, therefore, AB = CD.

AB = CD = 12 cm

CF = 1/2(CD)

CF = 1/2(12)

CF = 6 cm.

Learn more about the arc measure on:

https://brainly.com/question/2005046

#SPJ1

Step-by-step explanation:

[tex]\sf 12 \times \cfrac{12}{2} + 13[/tex]

First, let's divide 12 by 2:-

Multiply 12 × 6 :-

Add 72 + 13:-

Therefore, your answer is 85!!

____________________

Hope this helps!

Have a great day!!

Answer:

X-2=1

X-3=2

X+1=2

X+5=6

Distance of Park bench from building is 275 m when  angle of depression  top of the building to a park bench on the ground.

What is the elevation and depression angle?

Angle of depression, θ = 54°

The height, h = 200

The distance of park bench from the building, d is given by

Tan θ = opposite / Adjacent

Tan 54  = d / 200

d = 200 * Tan 54

d =  200 *  1.3764

d = 275.28

D = 275 M

Learn more about Angle of depression

brainly.com/question/13514202

#SPJ13

The correct equation is f(x) = 4x³ + 6x² − x .  A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

The value of the function is f(x). The slope of the line is m. b is either the function's value at x=0 or the position at which the line in the coordinate plane crosses the y-axis. x is the x-value. This form is called the slope-intercept form.

The slope of a linear function is calculated by rearranging the equation to its general form, f(x) = mx + c; where m is the slope.

in question f(-2) = - 6

so x= -2

In function f(x) = 4x³ + 6x² - x

F(-2) = 4(-2)³ + 6 (-2)² - (-2) = - 6

To learn more about function refer :

https://brainly.com/question/22340031

#SPJ1

Answer:

The slope of y = 5x - 4 is 5.

Notice that the equation, y = 5x - 4, of the line is written in the form y = mx + b. Thus, it is in slope-intercept form. When the equation of a line is in slope-intercept form, we know that the slope of the line is equal to m, the coefficient of x.

In y = 5x - 4, the coefficient of x is 5. Thus, the slope of the line, y = 5x - 4, is 5.

The proportion of American households who expect to buy a new car next year is[0.3191, 0.3609].

The Four answer choices:

[0.3152, 0.3648]

[0.3191, 0.3609]

[0.3394, 0.3406]

[0.3354, 0.3446]

According to the survey, 1,400 American households are expected to buy a new car next year. According to respondents, 34% plan on buying a new car next year.

The confidence interval for a population proportion is given by the following equation for large random samples

Sample proportion ± z × [tex]\frac{\sqrt{(sample proportion(1-sample proportion)}}{n}[/tex]

whereas z is a multiplier number that comes from the normal curve and determines the level of confidence.

To Learn more about Such Similar Proportion Questions:

https://brainly.com/question/28014021

#SPJ4

Answer: 32130000

Step-by-step explanation:

Multiply all of your numbers

Using the elimination method, the solution to the system of linear equations is: x = 4.5 and y = -5.

Solving a system of linear equations by elimination involves eliminating one of the variables, then solve to find the other variable.

Given the equations:

6x + 5y = 2 --> eqn. 1

4x + 2y = 8 --> eqn. 2

Multiply eqn. 1 by 2 and eqn. 2 by 5:

12x + 10y = 4 --> eqn. 3

20x + 10y = 40 --> eqn. 4

Subtract

-8x = -36

x = 4.5

Substitute x = 4.5 into eqn. 2

4(4.5) + 2y = 8

18 + 2y = 8

2y = 8 - 18

2y = -10

y = -5

The solution is: x = 4.5 and y = -5.

Learn more about system of linear equations on:

https://brainly.com/question/14323743

#SPJ1

The equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p are (b) 2.3p – 10.1 = 6.49p – 4 and (c) 230p – 1010 = 650p – 400 – p

The equation is given as

2.3p – 10.1 = 6.5p – 4 – 0.01p

Evaluate the like terms on the right-hand side

So, we have the following representation

2.3p – 10.1 = 6.49p – 4

The above equation is indicated in option (b)

Multiply through the equation by 100

So, we have:

100(2.3p – 10.1 = 6.5p – 4 – 0.01p)

Evaluate

230p – 1010 = 650p – 400 – p

The above equation is indicated in option (c)

Hence, the equations with the same solution are (b) and (c)

Read more about equivalent equations at

brainly.com/question/2972832

#SPJ1

Answer:

9/4

Step-by-step explanation:

(y + 7) = -2/3(x - 1) is the point-slope form of the equation of a line passing through (1, -7) and having a slope of -2/3.

The query revealed information include

a slope of -2/3

point (1, -7)

Those functions with exponents of 1 are known as linear functions.

The form represents the equation of a line in point-slope form.

(y - y₁) = m (x - x₁)

Variables in the y direction are described by  (y and y₁).

variables in the x direction are described by (x and x₁).

m = slope

substituting into the slope and point (1, -7) equation gives

()y + 7) = -2/3 (x - 1)

Learn more about linear functions at:

brainly.com/question/29213643

#SPJ1

The rule in expressed in function notation and slope-intercept form of a line is f(x) = 3x -2

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The equation of a line in slope-intercept form is y = mx + c.

Where m is the slope and c is the intercept

In order to obtain the equation of the line, we are going to pick any two convenient values of x and y from the table. Let's pick the first and last point. Thus:

point1: x₁ = 1, y₁  = 1

point2: x₂ = 4, y₂ = 10

Using the equation for 2 points:

y-y₁ / y₂-y₁ =  x-x₁ / x₂-x₁

y-1 / 10-1 = x-1 / 4-1

y-1 / 9 = x-1 /3

3(y-1) = 9(x-1)

y-1 = 3(x-1)

y-1 = 3x -3

y = 3x -3+1

y = 3x - 2

Thus, f(x) = 3x -2

Therefore, the rule in function notation, using the slope-intercept form of a line is f(x) = 3x -2

Learn more about the slope-intercept form equation of a line on:

brainly.com/question/29213312

#SPJ1

He can fill a total of 25 bags.

The values are,

50 blueberry scones total.

75 cranberry scones total.

For each bag to have an equal quantity of blueberry scones & cranberry scones, he must determine the maximum amount of bags he can fill.

H.C.F. of 50 & 75 is thus 25.

As a result, he can fill 25 bags.

There would be scones with blueberries in each bag of

50 ÷ 25 = 2

There would be cranberry scones for each bag, for a total of

75 ÷ 25 = 3

As a result, he may fill a total of 25 bags.

Learn more about the greatest common factor at

https://brainly.com/question/2190808?referrer=searchResults

#SPJ4

The description of the motion of the ant which is a geometric series is as follows;

a) After covering 63/32 meters, the ant will have made 6 turns

b) The distance the ant will eventually travel is 2 meters

Geometric series is an infinite sum of terms in which the ratio between consecutive terms is a constant.

The distances traveled by the ant is a geometric progression of the form;

The sum of the distance is given by the sum of the geometric progression as follow;

[tex]S_n = \dfrac{a\cdot \left(1 - r^n \right)}{(1 - r)}[/tex]

Where;

aₙ = The distance traveled in the nth turn

Sₙ = The sum of the distances

a = The first term = 1 meter

r = The value of the common ratio = 0.5 meter ÷ 1 meter = 0.5

a) The number of turns the ant will have made after covering a distance of 63/32 meters is therefore;

[tex]S_n =\dfrac{63}{32} = \dfrac{1\times \left(1 - 0.5^n \right)}{(1 - 0.5)}[/tex]

31.5 = 32 × (1 - 0.5ⁿ)

32 × 0.5ⁿ = 32 - 31.5 = 0.5

0.5ⁿ = 0.5 ÷ 32

n = ln(0.5 ÷ 32) ÷ ln(0.5) = 6

b) The distance the ant travels eventually is given by the formula for the sum to infinity of a geometric progression as follows;

[tex]S_{\infty} = \dfrac{a}{1-r}[/tex]

Which gives;

[tex]S_{\infty} = \dfrac{1}{1-0.5} = 2[/tex]

The distance the ant eventually travels is 2 meters

Learn more about geometric series and progression here:

https://brainly.com/question/27027925

#SPJ1

Answer:

The answer is w= -1

Step-by-step explanation:

4w + 2 + 0.6w = -3.4w - 6

4.6w + 2 = -3.4w - 6

8w + 2 = -6

8w = -8

w = -1

The solution is Pack #1

The pack which offers Toby the best deal is Pack #1

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the price per card of each pack be = A

Now , the equation is

a)

Pack #1

The number of cards = 12 cards

The cost per pack = $ 29

The equation is

So , the cost of 1 card = cost per pack / number of cards

                                    = $ 2.416

Therefore , the cost of one card in pack 1 is $ 2.416

b)

Pack #2

The number of cards = 24 cards

The cost per pack = $ 89

The equation is

So , the cost of 1 card = cost per pack / number of cards

                                    = $ 3.708

Therefore , the cost of one card in pack 2 is $ 3.708

c)

Pack #3

The number of cards = 24 cards

The cost per pack = $ 213

The equation is

So , the cost of 1 card = cost per pack / number of cards

                                    = $ 8.875

Therefore , the cost of one card in pack 3 is $ 8.875

And ,

cost of one card in pack 3 is $ 8.875 > cost of one card in pack 2 is $ 3.708 > cost of one card in pack 1 is $ 2.416

Therefore , the cost of one card in pack 1 is $ 2.416 and this is the best deal

Hence , The pack which offers Toby the best deal is Pack #1

To learn more about equations click :

https://brainly.com/question/10413253

#SPJ1

0.5  is the p-value for this Z -test .

What is the Z test's p-value?

For a lower tail test, the test statistic z is determined to be zero that means

P(z<0)

Then p-value is

p-value = P(z<0) = 0.5 (From z score table )

Learn more about p-value in Z test.

brainly.com/question/13686040

#SPJ4

The equation of the line that is parallel to the given line and passes through the point (-3,1) is y - 1 = 3/2(x + 3)

The line is passing through (-2, -4) and (2, 2)

The slope of the line is change in y coordinate with respect to the change in x coordinate of the line
Slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

Slope of the line = (2--4) / (2--2)

= 6/2

= 3/2

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

The point is given that (-3, 1)

The slope of the line = 3/2

because both are parallel lines

Substitute the both values in the equation

y - 1 = 3/2( x - (-3))

y - 1 = 3/2(x + 3)

Hence, the equation of the line that is parallel to the given line and passes through the point (-3,1) is y - 1 = 3/2(x + 3)

Learn more about point slope form here

brainly.com/question/14331653

#SPJ1

Answer:

y – 1 = 3/2(x + 3)

Step-by-step explanation:

The corresponding sides and angles of both the triangles [pre-image and the image] are congruent

Hence,The corresponding sides and angles of both the triangles [pre-image and the image] are congruent

learn more about congruency here:

https://brainly.com/question/1675117

#SPJ13