The probability that it rains is about 20%.
The probability that the bus is late is about 8%.
The probability that it rains and the bus is late is about 3%.
The probability that the train is late is about 5%.
The probability that it rains and the train is late is about 1%.

6. To decide whether the rain and the train running late are dependent or independent events, first define the two events and then write their probabilities as decimals. (3 points) Let event A = ________________________. P(A) = ______. Let event B = ________________________. P(B) = ______. A and B = ________________________. P(A and B) = ______. 7. Use the probabilities from question 6 to decide whether the rain and the train running late are independent or dependent events. (2 points: 1 point for the correct math, 1 point for the conclusion)

The polynomial remainder theorem states that the remainder of the division of a polynomial [tex]P(x)[/tex] by [tex]x-a[/tex] is equal to [tex]P(a)[/tex].

Therefore

[tex]P(-2)=4\\2\cdot(-2)^3 - 4\cdot(-2)^2 + k\cdot(-2) + 10=4\\-16-16-2k=-6\\-2k=26\\k=-13[/tex]

Answer:

Since both companies have a different plan, two equations are created to determine which company Jonas should choose with respect to the number of messages sent.

Step-by-step explanation:

- Sprint = $ 29.95 * X (0.15)

- AT & T = $ 4.95 * X (0.39)

One dollar equals 100 cents, so 0.15 cents equals $ 0.0015 dollars.

- Sprint = $ 29.95 * X (0.0015)

- AT & T = $ 4.95 * X (0.0039)

Si Jonas envía 500 mensajes de texto el valor mensual de cada empresa sería de:

- Sprint = $ 29.95 * 500 (0.0015)  = 22.46 dollar per month.

- AT & T = $ 4.95 * 500 (0.0039)  = 9.65 dollar per month.

The company Jonas should choose is AT&T.

AT&T also charges a little more per number of text messages, but since the phone's value is so low it would take thousands of text messages to compare to Sprint's monthly value.

Answer:

The Answer would be ∠W ≅ ∠C

Step-by-step explanation:

Only one that is congruent

The measure of the angle ∠TWM is congruent to the measure of the angle ∠ADC. Therefore, the correct option is B.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

A triangle is a three-sided polygon with three edges and three vertices in geometry.

Given that the triangle ∆MTW is congruent to the triangle ∆CAD.

So, we have

∠MTW ≅ ∠CAD

∠WMT ≅ ∠DCA

∠TWM ≅ ∠ADC

If two triangles are equivalent, the ratio of matching sides will stay constant.

The proportion of the point ∠TWM is harmonious with the proportion of the point ∠ADC.

Therefore, at that point, the right choice is B.

Learn more about congruent triangles here:

brainly.com/question/4364353

#SPJ3

Answer:

[tex]\huge\boxed{Option \ D}[/tex]

Step-by-step explanation:

4x + 5x = 180 [They are angles on a "straight" line so they will add up to 180 degrees)

Answer:

D

Step-by-step explanation:

The sum of angles that are formed on a straight line is 180.

4x + 5x = 180

Answer:

AandB=80miles

Total=240miles

Step-by-step explanation:

Draw the figure first indicating the figures then find the distance each degrees then find the total

The distance ship travels from A to B is 273.2 miles and total distance covered by ship is  707.82 miles.

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.

Given distance from C to A = 100 miles north

From B to A ship travels 60° east of north,

and From B to C 45° west of south,

the figure for problem is attached,

from figure we can  calculate the angles of A, B and C

so ∠A makes supplementary with 60°

∠A + 60° = 180°

∠A = 120°

for ∠B we need to draw an imaginary perpendicular on the line extending from A, we get

∠B + 45° + 30° = 90° (30° is angle of imaginary right triangle)

∠B = 90 - 75 = 15°

and ∠C can be found by,

∠A + ∠B + ∠C = 180°

∠C = 180 - 15 - 120

∠C = 45°

now use sine formula for triangles,

sinA/a = sinB/b = sinC/c

where A, B and C are angles of triangle and a, b and c are length of opposite side of angle A, B and C respectively.

a = BC, b = AC, and c = AB

so

sinA/BC = sinB/AC = sinC/AB

we have AC = 100 miles

substitute the values

sinC/AB = sinB/AC

sin(45)/AB = sin(15)/100

AB = 100/(√2sin(15))

AB = 100/0.3659

AB = 273.298 miles

and sinA/BC = sinB/AC

BC = AC sinA/sinB

BC = 100(sin 120/sin15)

BC = 100(0.866/0.2588)

BC = 100 x 3.3462

BC = 334.62 miles

total distance = AB + BC + AC

total distance = 334.62 + 273.2 + 100

total distance =  707.82 miles

Hence the distance from A to B is 273.2 miles and total distance is 707.82 miles.

Learn more about  laws of sines;

https://brainly.com/question/17289163

#SPJ2

Answer:

x = 7

Step-by-step explanation:

4x + 5 = x + 26

4x - x = 26 - 5

3x = 21

x = 21/3

x = 7

Check:

4*7 + 5 = 7 + 26

28 + 5 = 33

Answer:

[tex]\huge\boxed{Supplementary \ Angle}[/tex]

Step-by-step explanation:

118 is a supplementary angle. It is not a complementary angle because complementary angles add up to 90 and 118 is greater than 90 degrees. So, 118 is a supplementary angle and it is an angle adding up to 180 degrees with any other angle measuring 62 degrees.

Answer:Supplementary

Step-by-step explanation:You should remember that complementary refers to any number from 0-90 and supplementary refers to any number from 90 onwards..

Hereby giving the answer as ''Supplementary''

Answer:

To find the median you cross off the first few numbers and the last few until you get to the middle then when you get the middle number that will be your median

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

It's the middle value of a list of numbers arranged in order.

For example the median of the list 1 2 3 4 5 is 3.

If there are an even number of values, the median is the mean of the middle two. For example:

1 3 4 5 7 9:

The middle 2 numbers are 4 and 5 so

the median is  (4 + 5) / 2 = 4.5

Answer:

Step-by-step explanation:

23x +2 = 15x+48x+6

To solve for x group like terms

That's

Send the constants to the right side of the equation and those with variables to the left side

We have

23x - 15x - 48x = 6 - 2

Simplify

- 40x = 4

Divide both sides by -40

We have the final answer as

Hope this helps you

Answer:

C

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The lower quartile range is shown by the bottom of the box which is at 10.

The median is shown in the middle line, which is closer to 18 than 18.5.

The upper quartile range in the end of the box, which is at 22!

(You can also look at the picture attached if that helps.)

Answer:

slope - (2x)

y-intercept - (-1)

Step-by-step explanation:

-8x + 4y = - 4

4y = 8x - 4

y = 2x - 1

Answer:

4.44 pints

Step-by-step explanation:

7.4 times 3/5

Answer:

A, C

Step-by-step explanation:

Only B is containing a variable .

The  -5 is not variable.

We have given that,

A.3x2

B. y

A

C. -5

In the expression 3x^2 + y -5

We have to determine which of the following terms does not have a variable.

variable, In algebra, a symbol stands in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).

Only C contains a variable.

The  -5 is not variable.

To learn more about the variable visit:

https://brainly.com/question/2804470

#SPJ2

Answer:

2 hrs, 24 min

Step-by-step explanation:

Sally:  in one hour, she can paint 1/4 of the room.

Joe: in one our, he can paint 1/6 of the room

Hour one: 1/4+1/6=3/12+2/12=5/12

1÷5/12=1*12/5=12/5

12/5= 2 & 2/5 hours, or 2.4 hours, or 2 hrs 24 minutes

Answer: 2.4 hours

Step-by-step explanation:

1/4 1/6

LCM

3/12+2/12=5/12 repricical 12/5 =2.4

Answer:

The answer is

Step-by-step explanation:

From the question

[tex]\alpha[/tex] is inversely proportional to [tex]\beta[/tex] is written as

where k is the constant of proportionality

When

Substituting the values into the formula

we have

[tex]4 = \frac{k}{9} [/tex]

cross multiply

k = 4 × 9

k = 36

So the formula for the variation is

[tex] \alpha = \frac{36}{ \beta } [/tex]

when

[tex]\beta[/tex] = - 72

That's

[tex] \alpha = \frac{36}{ - 72} [/tex]

Simplify

We have the final answer as

Hope this helps you

Answer:

6 sacks

Step-by-step explanation:

Buying Price = $1200

Selling Price = $1500

Total profit = Selling price - Buying Price

= $1500 - $1200

= $300

Given that the profit on each sack of tea is $50

Number of Sacks of Tea = Total Profit ÷ profit per sack

= $300 ÷ 50

= 6 sacks

The number of sacks of tea he has is 6.

The first step is to determine the total profit earned by the trader. Profit is the selling price less the cost price.

Profit = selling price - cost price

$1500 - $1200 = $300

The second step is to divide the total profit by the profit made per sack of tea.

Number of sacks = $300 / $50 = 6

To learn more about division, please check: https://brainly.com/question/194007

Answer:

Hey there!

The overlapping part is the product.

Thus, the product is 1/8.

Hope this helps :)

Answer:

-1, 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

answer is (-1,4)

Answer:

x = 15.9

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hyp

cos 28 = 14/x

x  cos 28 = 14

x = 14 / cos 28

x=15.85598

Rounding to the nearest tenth

x = 15.9

Answer:

7 divided by 4 is 1 ¾ as a fraction, or 1.75 as a decimal.

Step-by-step explanation:

Pls mark as brainliest answer

The calculated division of the numbers seven divided by 4 is 1 3/4

From the question, we have the following parameters that can be used in our computation:

seven divided by 4

When represented as an equation, we have

seven divided by 4 = 7/4

Divide 7 by 4

So, we have the following result

seven divided by 4 = 1 3/4

Using the above as a guide, we have the following:

the result is 1 3/4

Read more about quotient at

brainly.com/question/11418015

#SPJ6

Answer:

GREAT QUESTION!!

Step-by-step explanation:

Bases of exponential functions CANNOT be 1.

It the base was between 0 and 1, .25 for example, then it would be exponential decay, because as x would increase y would decrease.

Just search up exponential decay to see what it looks like, or type in y=.25^x in google search bar.

if this helped, Please give brainly, I need it! Thank you!

Answer:

If the base of the exponent were 1, the function would remain constant. The graph would be a horizontal line. If the base of the exponent were less than 1, but greater than 0, the function would be decreasing.

Step-by-step explanation:

If the base were 1, the function would be constant.

If the base were 1, the graph would be a horizontal line.

If the base were between 0 and 1, the function would be decreasing.

Answer:

Approximately 439.6 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cone is the following:

[tex]A=\pi r^2+\pi r l[/tex]

Where, r is the radius and l is the slant height.

The radius is 7 and the slant height is 13. We also use 3.14 for π Thus:

[tex]A=(3.14)(7)^2+(3.14)(7)(13)\\\text{Use a Calculator}\\A\approx 439.6[/tex]

Answer:

292.77

Step-by-step explanation:

πr(r+[tex]\sqrt{h2+r2}[/tex])

13 x 2 = 26

7 x 2 = 14

26 + 14 = 40

[tex]\sqrt{40}[/tex] = 6.32

7 + 6.32 = 13.32

3.14 x 7 = 21.98

21.98 x 13.32 =

292.77

Answer:

  37.5 mi/h

Step-by-step explanation:

  time = distance / speed

On the trip 'going', the time was (150 mi)/(50 mi/h) = 3 h.

On the return trip, the time was (150 mi)/(30 mi/h) = 5 h.

__

  speed = distance / time

The average speed for the whole trip was ...

  speed = (150 mi +150 mi)/(3 h +5 h) = (300 mi)/(8 h) = 37.5 mi/h

His average rate of speed was 37.5 miles per hour.

Answer:

3x+11y-3

Step-by-step explanation:

Hey! So here is what you do to solve the problem-

Combine like terms:

(x) 5x-2x=3x

(y) 3y+8y=11y

(#) 7-10 =-3

So....

3x+11y-3 is your answer!

Hope this helps!:)

Answer:

43

Step-by-step explanation:

Using Thales theorem:

● SP/LN = RP /RN

Notice that RN = 2×RP

● SP/LN = RP/2RP

● SP /LN = 1/2

● SP / (5x-14) = 0.5

● (2x+3)/(5x-14) = 0.5

● 2x+3 = 0.5(5x-14)

● 2x+3 = 2.5x -7

Add 7 to both sides

● 2x+3+7 = 2.5x-7+7

● 2x+10 = 2.5x

Sustract 2x brom both sides

● 2x+10-2x = 2.5x-2x

● 10 = 0.5x

Multiply both sides by 2

● 10×2 = 0.5x×2

● 20 = x

Replace x with 20 in Sp expression:

● SP = 2x+3

● SP = 2×20+3

● SP = 43

Answer:

The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is at (-2, 2)

The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is at (3, -1)

The coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is at (4, -2)

The coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is at (4, 2)

Step-by-step explanation:

A transformation is the movement of a point from its initial position to a new position. If a shape is transformed, all its points are also transformed. Types of transformation are reflection, rotation, dilation and translation.

Given Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2).

If a point X(x, y) is rotated 90° counterclockwise, the new location X' is at (-y, x)

If a point X(x, y) is rotated 90° clockwise, the new location X' is at (y, -x)

If a point X(x, y) is rotated 180° clockwise, the new location X' is at (-x, -y)

If a point X(x, y) is rotated 270° counterclockwise, the new location X' is at (y, -x)

The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is at (-2, 2)

The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is at (3, -1)

The coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is at (4, -2)

The coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is at (4, 2)

Answer:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If a point A(x, y) is rotated 90° counterclockwise, the new point is at A'(-y, x).

If a point A(x, y) is rotated 90° clockwise, the new point is at A'(y, -x). If a point A(x, y) is rotated 180° counterclockwise, the new point is at A'(-x, -y).

If a point A(x, y) is rotated 270° counterclockwise, the new point is at A'(y, -x).

Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2).

The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is D'(-2, 2)

The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is C"(3, -1).

The coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is A''"(4, -2)

The coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is B"(4, 2)

Answer:

22 units²

Step-by-step explanation:

1/2b*h=area

You can either count the units or use the distance formula.

[tex]d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]

b = 4 units

h = 11 units

area = (1/2*4)*11 = 22 units²

Answer:

Option C.

Step-by-step explanation:

It is given that,

[tex]P(A)=\dfrac{1}{4}[/tex]

[tex]P(B)=\dfrac{13}{20}[/tex]

It is given that events A and B are mutually exclusive. It means they have no common elements.

[tex]P(A\cap B)=0[/tex]

We know that,

[tex]P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

On substituting the values, we get

[tex]P(A\cup B)=\dfrac{1}{4}+\dfrac{13}{20}-0[/tex]

[tex]P(A\cup B)=\dfrac{5+13}{20}[/tex]

[tex]P(A\cup B)=\dfrac{18}{20}[/tex]

[tex]P(A\cup B)=\dfrac{9}{10}[/tex]

Therefore, the correct option is C.

The P (A or B) should be [tex]\frac{9}{10}[/tex]

Given that,

Based on the above information, the calculation is as follows:

[tex]= \frac{1}{4} + \frac{13}{20}\\\\= \frac{5+13}{20} \\\\= \frac{18}{20}\\\\= \frac{9}{10}[/tex]

Learn more: https://brainly.com/question/17429689?referrer=searchResults

distance of a point [tex](x,y)[/tex] from origin is $\sqrt{x^2+y^2}$

so distance is $\sqrt{(-15)^2+(8)^2}=\sqrt{225+64}=\sqrt{289}=17$

Answer:

Distance=17 units

Step-by-step explanation:

Coordinates of the origin: (0, 0)

Coordinates of the point in question: (-15, 8)

Distance formula for any two points [tex](x_1,y_1), (x_2,y_2)[/tex] on the plane:

[tex]distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance=\sqrt{(-15-0)^2+(8-0)^2}\\distance=\sqrt{(15)^2+(8)^2}\\distance=\sqrt{225+64} \\distance=\sqrt{289} \\distance=17[/tex]

Answer:

It is reduced to the equation of the Theorem of Pythagoras.

Step-by-step explanation:

Any triangle can be modelled by this formula under the Law of Cosine:

[tex]b = \sqrt{a^{2}+c^{2}-2\cdot a\cdot c\cdot \cos B}[/tex]

Where:

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Side lengths, dimensionless.

[tex]B[/tex] - Angle opposed to the side [tex]b[/tex], measured in sexagesimal degrees.

Now, let suppose that angle B is a right angle (90º), so that b is a hypotenuse and a and c are legs. Hence:

[tex]\cos B = 0[/tex]

And the equation is reduced to the form of the Theorem of Pythagoras, that is to say:

[tex]b = \sqrt{a^{2}+c^{2}}[/tex]