If the radius of the circle is decreased by a factor of One-third, what happens to the circumference?
The circumference decreases by a factor of One-third.
The circumference decreases by a factor of 3.
The circumference increases by a factor of One-third.
The circumference increases by a factor of 3.

Answer:

probability that the page opened will start with S

Step-by-step explanation:

14/90

0.15556

Answer:

A) P(F) = 0.124

B) P(S|F) = 0.8065

C) P(V|F^(c)) = 0.886

Step-by-step explanation:

Let us denote as follows;

F = Message contains word free

S = message is spam

V = message is valid

From the question, we are given that;

The probability that word free occurs in spam messages;P(F|S) = 50% = 0.5

The probability of the valid messages that contain free; P(F|V) = 3% = 0.03

Spam messages; P(S) = 20% = 0.2

Valid messages; P(V) = 1 - 0.2 = 0.8

A) From rule of total probability ;

probability that the message contains the word free is given as;

P(F) = P(F|S)•P(S) + P(F|V)•P(V)

P(F) = (0.5 x 0.2) + (0.03 x 0.8)

P(F) = 0.124

B) From Baye's theorem;

probability that the message is spam given that it contains free is given as;

P(S|F) = P(F|S)•P(S)/P(F)

P(S|F) = (0.5 x 0.2)/0.124

P(S|F) = 0.8065

C) From combination of complement rule and Baye's theorem;

probability that the message is valid given that it does not contain free is given as;

P(V|F^(c)) = P(F^(c)|V)•P(V)/P(F^(c))

Thus,

P(V|F^(c)) = [(1 - P(F|V))•P(V)]/(1 - P(F))

P(V|F^(c)) = ((1 - 0.03)•0.8)/(1 - 0.124)

P(V|F^(c)) = 0.776/0.876

P(V|F^(c)) = 0.886

Answer:

simplify question is 3a^2 +6a+9ab

Step-by-step explanation:

Answer:

The answer to your question is below

Step-by-step explanation:

Process

To answer if they are right triangles or not use the Pythagorean theorem which states that the square of the hypotenuse equals the sum of the square of the legs.

a)    25² = 20² + 7²

      625 = 400 + 49

     625 ≠ 449              It is not a right triangle

b)   26² = 24² + 10²

      676 = 576 + 100

      676 = 676               it is a right triangle

c)   13² = 8² + (√10)²

     169 = 64 + 10

      169 ≠ 74                 it is not a right triangle

d)   52² = 48² + 20²

      2704 = 2304 + 400

      2704 = 2704               it is a right triangle

Answer:

P = 2(21 + 3)

= 2(24)

=$48

Step-by-step explanation:

Add them all up.

s + 2(s+3) + 4s-5 = 148

s + 2s + 6 + 4s - 5 = 148

Group all s together and all numbers together 7s + 1 = 148

7s = 147

Divide by 7

s = 21

Plug s=21 back in for Petro

To find the amount of money in Pertro's account, use the equation x = 148 - (y + z), where y and z represent the amounts in the other two accounts.

The equation to find the amount of money in Pertro's account can be written as:

x + y + z = 148

where x, y, and z represent the amounts in different accounts. To find the amount in Pertro's account, we need to set up another equation using the information given. If we know that the total of all accounts is $148 and we want to find the amount in Pertro's account (x), we can write:

x = 148 - (y + z)

where y and z represent the amounts in the other two accounts.

https://brainly.com/question/17595716

#SPJ2

Answer:

x=5 feet

Step-by-step explanation:

At floor level y=0

If the expression is:

[tex]0=1/3(x-5)(x+5)\\0=1/3(x^2-25)\\0=1/3x^2-25/3\\25/3=1/3x^2\\25=x^2\\x=5[/tex]

But, with the negative sign, the answer is x= 5i (where i is imaginary)

Final answer:

The width of the arch at floor level is found by determining the points where the parabola intersects the x-axis, which are at x = 5 and x = -5. The width is the distance between these points, which is 10 feet.

Explanation:

To find the width of the arch at floor level, we need to determine the distance between the two points where the parabola represented by the equation y = -1/3(x-5)(x+5) intersects the x-axis. The x-axis represents the floor, and the points of intersection occur where y is equal to 0.

Setting the equation to 0 gives:

0 = -1/3(x-5)(x+5)

By solving for x, we get x = 5 and x = -5, which are the points where the parabola intersects the x-axis. The distance between -5 and 5 on the x-axis is 10 feet, so the width of the arch at floor level is 10 feet.

Answer:

3/13

Step-by-step explanation:

There are 52 card in a deck of cards

12 of them are face cards   3 cards *4 suits =12

P (face card) = 12/52 = 3/13

Answer:1/3 decimal form: 0.333 repeating percent: 3.33%

Answer:

3 swimmers

Step-by-step explanation:

Answer:

The correct option is;

A. The mean speed and the range of the speeds of the motorists decreased

Step-by-step explanation:

Here we have the speeds given as

                  Before Sign Installation

Speed                                                   Frequency

20                                                             1

24                                                             1

25                                                             4

30                                                             2

35                                                             2

38                                                             1

40                                                             1

∑ 212                                                        12

Mean = 17.67

Median (25 + 30)/2 = 27.5

Range  = 40 - 20 = 20

                     After  Sign Installation

Speed                                                   Frequency

20                                                             1

22                                                             1

25                                                             4

28                                                             1

30                                                             3

35                                                             2

∑ 160                                                        12

Mean = 160/12 = 13.33

Median = (25+28)/2 = 26.5

Range  = 35 - 20 = 15.

Therefore, the mean speed and the range of the speeds of the motorists decreased

Answer:

1/22 gallons per mile

Step-by-step explanation:

We want to find gallons per mile, so we take the gallons and divide by the mile

10gallon/ 220 mile

1/22 gallons per mile

Answer:

1/22 gallons per mile

Step-by-step explanation:

Step-by-step explanation:

(c)

[tex] In\: \triangle PLM \: \&\: \triangle PLM\\

\angle PLM \cong\triangle PFG.. (corresponding \:\angle s) \\

\angle LPM \cong \angle FPG.. (common \: \angle s) \\

\therefore \triangle PLM\sim\triangle PFG.. (by\: AA\:Postulate) \\

PF = PL + LF = 2 + 3 = 5[/tex]

By area of similar triangle theorem:

[tex] \frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{PL^2}{PF^2}\\

\therefore \frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{2^2}{5^2}\\

\therefore \frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{4}{25}\\

A(\triangle PLM)\: :\: A(\triangle PFG) = 4 \: :\: 25

[/tex]

Answer:

18.00 dollars

Step-by-step explanation:

message me if you need help. Or this was not the answer you were looking for.

Answer:

see below

Step-by-step explanation:

Tally question

There are 6 marks for A out of 30 total

6/30 = 1/5

Sample space question

{run 50  run 100 run 150, swim 50 swim 100 swim 150}

We have to list all the possible choices that the spinners can land

run         50

swim      100

               150

There are 2*3 = 6 choices

Tomas Game

1/36

The normal die has 1,2,3,4,5,6

P(5) = Number of 5's / total number of numbers = 1/6

Then roll another 5

P(5) = Number of 5's / total number of numbers = 1/6

P(5,5) = 1/6*1/6 = 1/36

Joe game

1/4

1,2,3,4,5,6  triangle, square

P(0dd) = {1,3,5}/ 6 numbers = 3/6 = 1/2

P (square) = square/ total  = 1/2

Coin

1/2

HT HH TH TT

We want one heads and one tails

2 of the four

2/4 = 1/2

P (odd,square) = P(odd) * P(square) = 1/2*1/2 = 1/4

Answer:

1) ⅕

2) sample space: D

3) 1/36

4) P(odd & square) = ¼

5) ½

Step-by-step explanation:

1) P(A) = 6/30 = 1/5

2) sample space is the collection of all possible outcomes

{activity & distance}

3) P(5 & 5) = 1/6 × 1/6

1/36

4) odd: 1,3,5

P(odd) = 3/6 = 1/2

P(square) = 1/2

1/2 × 1/2 = 1/4

5) P(H & T) = 1/2 × 1/2 = 1/4

2 × 1/4 = 1/2

Answer:

16.56‬

Step-by-step explanation:

The area of the square is 2 × 2

The area of the circle is-

A=πr²

A=3.14 × 2²

A=3.14 × 4

A=12.56

You don't need to divide it by half because there are two half circles so it would be a whole circle

12.56 + 4 = 16.56

Sorry if it is wrong

Answer:

Area of square =side( square)

(2) square

4

diameter= 2

radius=2/2

= 1

Area of circle=πrsquare

22/7×1×1

3.14

Area of figure= Area of square+area of circle

4+3.14

7.14

Answer:

64

Step-by-step explanation:

The first thing I would do is break down the question and put it into number form. 2/3 of the jelly beans are black. You want to find out the number of jelly beans out of 96 are black. I can try my best to explain how to do this.

Divide the number of jelly beans (96) by the denominator (3) to find out how many jelly beans would be 1/3. This is 32. To find out how many are 2/3 you would multiply the 1/3 (32) by 2 to find that it is 64.

To check your work simplify this. 64/96 and it should equal 1/3. Or put it in your calculator to find that it equals .667 which is the decimal form of 2/3.

Answer:

Since you provided no graphs, I just graphed y=(x+3)(x+3). I hope this helps.

Final answer:

The graph defined by the function y = (x+3)(x+3) is a parabola opening upwards with its vertex at (-3, 0), represented by a U-shaped curve on the coordinate plane.

Explanation:

The function given by y = (x+3)(x+3) represents a quadratic equation, which can be expanded to y = x^2 + 6x + 9. This is a parabola that opens upwards because the coefficient of the x^2 term is positive. The graph of this function will have its vertex at the point (-3, 0), which is obtained by setting the inside of the parentheses to zero. To visualize this function, you would plot a series of points by choosing different values for x, calculate the corresponding y values, and then plot these points on a coordinate plane. Connecting these points will reveal the U-shaped curve typical for a quadratic function.

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

You know:

m = [tex]\frac{1}{3}[/tex]      So substitute/plug it into the equation

y = mx + b

[tex]y=\frac{1}{3} x+b[/tex]   To find b, plug in the point (-6, 0) into the equation, the isolate/get the variable "b" by itself

[tex]0=\frac{1}{3} (-6)+b[/tex]

0 = -2 + b         Add 2 on both sides to get "b" by itself

0 + 2 = -2 + 2 + b

2 = b

[tex]y=\frac{1}{3} x+2[/tex]       Your answer is the 4th option

The equation in slope-intercept form is y = 1/3x  + 2

The equation of the line in point slope form is expressed as:

where:

Substitute:

y - 0 = 1/3(x+6)

Write in slope-intercept form

y = 1/3(x+6)

3y = x + 6

y = 1/3x + 6/3

y = 1/3x + 2

Hence the equation in slope-intercept form is y = 1/3x  + 2

Learn more on slope-intercept here: https://brainly.com/question/19440459

Answer:

119°

Step-by-step explanation:

In circle with center B, JH is diameter.

[tex]m\angle GHI = 360° - (90° + 151°)\\

m\angle GHI = 360° - 241°\\

m\angle GHI = 119°\\

\because\overset{\frown}{GHI} =m\angle GHI\\

\huge \red{ \boxed{\therefore \overset{\frown}{GHI} =119°}}\\ [/tex]

Answer:

7

Step-by-step explanation:

One side is half of the other (5/2.5=2)

So 14/2=7

To measure an angle using a protractor, follow these steps: Place the center point of the protractor at the vertex, align the base line with one side, and read the measure where the other side intersects the scale.

To measure an angle using a protractor, follow these steps:

For example, if the measure reads 45 degrees, then the angle is 45 degrees.

https://brainly.com/question/29898085

#SPJ12

The value of Pascale's savings account at the end of the fifth year, with a 7.5% interest rate compounded annually and an additional $500 deposited each year, is approximately $3,122.00.

To calculate the value of Pascale's account at the end of the fifth year, we must use the compound interest formula which is A = P (1 + r)^t, where:

However, since Pascale deposits an additional $500 at the beginning of each year, the calculation is more complex than a single application of the formula. Our calculation should reflect the compound interest earned on each individual $500 deposit, not just the initial deposit.

Let's calculate the value at the end of year 5 step by step, adding $500 at the beginning of each year:

Therefore, the value of the account at the end of the fifth year is approximately $3,122.00.

S=wl

0.24=wl

it can be w=0,6 and l=0,4 or w=0,4 and l=0,6

Answer:

n=4.28571429

Step-by-step explanation:

Solve for n by isolating it

7n=30

Divide both sides by 7 to "reverse" the multiplication being done to n

n=4.28571429

Answer "n" is 4 and 2 sevenths

Step-by-step explanation:

7n = 30 get "n" alone

7n / 7 = 30 / 7

n = 4 and 2/7

Answer:

24.

Step-by-step explanation:

The is the number of permutations of 3 digits from 4

= 4P3

= 4! / (4- 3)!

= 4 *3 *2 *1 / 1!

= 24/1

= 24.

Answer:

Yes, it will overflow, because the volume of the scoop of ice cream is higher than the volume of the cone.

Step-by-step explanation:

To know if the cone will overflow when the entire scoop of frozen yogurt melts, we need to compare the volume of the scoop and the volume of the cone: if the volume of the scoop is higher, it will overflow.

The volume of the cone is:

V_cone = (1/3)*pi*r^2*h

Where V_cone is the volume, r is the radius and h is the height. So:

V_cone = (1/3)*pi*2^2*6 = 25.1327 in3

The volume of a sphere is:

V_sphere = (4/3)*pi*r^3

Where V_sphere is the volume and r is the radius. If the diameter is 4, the radius is 4/2 = 2. So:

V_sphere = (4/3)*pi*2^3 = 33.5103 in3

The volume of the sphere is higher, so the cone will overflow.

The volume of the melted ice cream scoop[tex](\( 33.51032 \, \text{cubic inches} \))[/tex] is greater than the volume of the cone [tex](\( 25.13272 \, \text{cubic inches} \))[/tex] the cone will overflow if the entire scoop of ice cream melts into it.

Step 1: Volume of the Cone

The formula for the volume of a cone is:

[tex]\[V_{\text{cone}} = \frac{1}{3} \pi r^2 h\][/tex]

where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height.

Given:

[tex]\[r = 2 \, \text{inches}, \quad h = 6 \, \text{inches}\][/tex]

Substitute these values into the formula:

[tex]\[V_{\text{cone}} = \frac{1}{3} \pi (2)^2 (6)\][/tex]

[tex]\[V_{\text{cone}} = \frac{1}{3} \pi (4) (6)\][/tex]

[tex]\[V_{\text{cone}} = \frac{1}{3} \pi (24)\][/tex]

[tex]\[V_{\text{cone}} = 8 \pi \, \text{cubic inches}\][/tex]

Step 2: Volume of the Ice Cream Scoop

The formula for the volume of a sphere is:

[tex]\[V_{\text{sphere}} = \frac{4}{3} \pi r^3\][/tex]

where [tex]\( r \)[/tex] is the radius of the sphere.

Given that the diameter of the sphere is [tex]4\ inches[/tex], the radius [tex]\( r \)[/tex] is:

[tex]\[r = \frac{4}{2} = 2 \, \text{inches}\][/tex]

Substitute this value into the formula:

[tex]\[V_{\text{sphere}} = \frac{4}{3} \pi (2)^3\][/tex]

[tex]\[V_{\text{sphere}} = \frac{4}{3} \pi (8)\][/tex]

[tex]\[V_{\text{sphere}} = \frac{32}{3} \pi \, \text{cubic inches}\][/tex]

Step 3: Compare the Volumes

The volume of the cone:

[tex]\[V_{\text{cone}} = 8 \pi \, \text{cubic inches}\][/tex]

The volume of the ice cream scoop:

[tex]\[V_{\text{sphere}} = \frac{32}{3} \pi \, \text{cubic inches}\][/tex]

Let's convert them to decimal form for easier comparison:

[tex]\[V_{\text{cone}} = 8 \pi = 8 \times 3.14159 = 25.13272 \, \text{cubic inches}\][/tex]

[tex]\[V_{\text{sphere}} = \frac{32}{3} \pi = \frac{32}{3} \times 3.14159 = 33.51032 \, \text{cubic inches}\][/tex]

Answer:

Universal set ( U ) = Set of prime numbers

Step-by-step explanation:

Solution:-

- All even numbers are numbers that are divisible by 2 or have at-least an LCM of 2 associated with that number.

- All prime numbers are divisible by 1 and the number itself. Which 2 which is divisible by 1 and itself is a prime number and an even number.

- Considering only positive integers.

- Carrie is looking for a set of even numbers within the set of prime number.

- As stated above, the only integer, 2, is common to both prime number set and even number set.

- Hence, universal set ( U ) should be prime numbers.

- Universal set ( U ) = Set of prime numbers.

Answer:

c. prime numbers

Step-by-step explanation:

edg 2020

Answer:

61 67     71 73 79

There you go:)

Answer:

53, 59, 61, 67, 71.

Step-by-step explanation:

It goes on....

53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109

, 113, 127, 131, 137, 139

I hope this helps :)

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Equation               25x² + 64y² = 1600

Process

1.- Divide all the equation by 1600

                             25x²/1600 + 64y²/ 1600 = 1600/1600

-Simplify

                              x²/64 + y²/ 25 = 1

2.- Equation of a horizontal ellipse

                             [tex]\frac{x^{2} }{a^{2}} + \frac{y^{2}}{b^{2}} = 1[/tex]

3.- Find a, b and c

    a² = 64             a = 8

    b² = 25             b = 5

-Calculate c with the Pythagorean theorem

                   a² = b² + c²

-Solve for c

                   c² = a² - b²

-Substitution

                   c² = 8² - 5²

-Simplification

                  c² = 64 - 25

                  c² = 39

-Result

                  c = √13

4.- Find the center

          C = (0, 0)

5.- Find the vertices

          V1 = (-8, 0)     V2 = (8, 0)

6.- Find the foci

          F1 = (-√13, 0)   F2 = (√13, 0)

The center of the ellipse is (0,0), the vertices are (5.657, 0) and (-5.657, 0), and the foci are (3.317, 0) and (-3.317, 0).

The given equation of the ellipse is 25x^2 + 64y^2 = 1600.

To find the center of the ellipse, we can rewrite the equation in standard form: x^2/32 + y^2/25 = 1. The center is (0,0) since the x and y terms are squared and have the same coefficients.

To find the vertices of the ellipse, we can calculate the distance from the center to the major axis. The length of the major axis is 2*a, where a is the square root of the denominator of the x term. In this case, a = sqrt(32) ≈ 5.657. So the vertices are (5.657, 0) and (-5.657, 0).

To find the foci of the ellipse, we can calculate the distance from the center to the foci. The length of the foci is 2*c, where c is the square root of the difference between the squares of a and b (sqrt(32-25) ≈ 3.317). So the foci are (3.317, 0) and (-3.317, 0).

https://brainly.com/question/33868440

#SPJ3

Answer:

17

Step-by-step explanation:

5 x 5 is 25

6 x 7 42

25 + 42 is 67

67 - 50 = 17

17 is your answer :)

Answer:

The volume of the paper weight is 942.8 cubic cm.

Step-by-step explanation:

We are given the following in the question:

Dimensions of paperweight :

Radius, r = 10 cm

Height,h = 9 cm

Volume of paper weight = Volume of cone

[tex]V= \dfrac{1}{3}\pi r^2 h[/tex]

where r is the radius and h is the height of the cone.

Putting values, we get,

[tex]V = \dfrac{1}{3}\times \dfrac{22}{7}\times (10)^2\times 9\\\\V = 942.8\text{ cubic cm}[/tex]

Thus, the volume of the paper weight is 942.8 cubic cm.

The volume is 942.5 [tex]cm^{3}[/tex].

To calculate the volume of a cone, you can use the formula:

V = (1/3)πr²h

where:

1. For Marta's paperweight with a radius of 10 centimeters and a height of 9 centimeters, you substitute the values into the formula as follows:

V = (1/3)π(10 cm)²(9 cm)

2. First, calculate the base area:

(10 cm)² = 100 cm²

3. Then, multiply by the height:

100 cm² × 9 cm = 900 cm³

4. Finally, multiply by (1/3)π:

V = (1/3)π × 900 cm³ ≈ 942.5 cm³

Therefore, the volume of the cone is approximately 942.5 [tex]cm^{3}[/tex], rounded to the nearest tenth.