Consider an experiment in which a marble is tossed into a box whose base is shown in the figure. The probability that the marble will come to rest in the shaded portion of the box is equal to the ratio of the shaded area to the total area of the figure. If the probability is equal to 3/10, find the positive value of x.

Answer:

Step-by-step explanation:

The shaded regions consist of a triangle and a semicircle

Area of shaded regions = Area of Triangle + Area of semicircle

Area of Triangle = (h x b) ÷ 2

Height, h = 10 cm

Base, b = 8 cm

Are of the triangle component = (10 x 8) ÷ 2

= 80 ÷ 2

= 40 cm^2

 Area of semicircle = πr^2 ÷ 2

Diameter, D = 8 cm

Radius, r = 8 cm ÷ 2 = 4 cm

Are of the semicircle component = [π(4^2) ÷ 2)

= 16π ÷ 2

= 16π cm^2

 Total area of shaded regions

= (40+16π) cm^2

= 8 (5 +2π) cm^2

Answer:

[tex]\boxed{\sf Area = 8\pi + 40\ cm^2}[/tex]

[tex]\boxed{\sf Perimeter = 4\pi + 22\ cm}[/tex]

Step-by-step explanation:

Area of the figure:

Firstly: Area of semicircle:

[tex]\sf \frac{\pi r^2}{2} \\Where\ r = 4 \ cm\\\frac{\pi (4)^2}{2} \\\frac{16 \pi}{2}\\8 \pi \ cm^2[/tex]

Then Area of Triangle

[tex]\sf 1/2 (Base)(Height)\\1/2(10)(4)\\10*2\\20\ cm^2[/tex]

Area of Figure = Area of Semicircle + 2(Area of triangle)

=> 8π + 2(20)

=> 8π + 40 cm²

Perimeter of Semicircle:

Firstly, we'll have to find the hypotenuse

[tex]\sf c^2 = a^2+b^2\\c^2 = 4^2+10^2\\c^2 = 16+100\\c^2 = 116\\c = 11\ cm[/tex]

Then, Perimeter of the semi-circle:

=> πr

Where r = 4 cm

=> 4π

Now, the perimeter of the whole figure:

=> 4π + 2(11)

=> 4π + 22 cm

===============================================

Explanation:

Let's calculate the angle B based off the arcs CDF and GHJ

B = (far arc - near arc)/2

B = (arc CDF - arc GHJ)/2

B = (130 - 40)/2

B = 90/2

B = 45

----------

Now let's change GHJ to 30 degrees, while keeping the other arc the same.

B = (far arc - near arc)/2

B = (arc CDF - arc GHJ)/2

B = (130 - 30)/2

B = 100/2

B = 50

Angle B has increased from 45 degrees to 50 degrees.

Answer:

x = 80

Step-by-step explanation:

Tangent Chord Angle  =1/2 Intercepted Arc

40 = 1/2 x

80 = x

Answer:

x = 5

Step-by-step explanation:

The measure of an arc equals the measure of the central angle that intercepts it.

The measure of an arc intercepted by a diameter is 180 deg.

m(arc)EH = 180

m(arc)EF + m(arc)FG + m(arc)GH = m(arc)EH

10x + 8 + 67 + 11x = 180

21x + 75 = 180

21x = 105

x = 5

Answer:

1.) 3 shovels/7 buckets

2.)7 buckets/3shovels

Answer:

22.5

Step-by-step explanation:

cause

Answer:

It is 22.5

Step-by-step explanation:

add up all they shaded parts:

22.5 x 4 = 90 degrees

as each unshaded part is three times more then you do 22.5 x 3 for one part

22.5 x 3 = 67.5 degrees

then times by four because there is four unshaded sections.

67.5 x 4 = 270 degrees

270 + 90 = 360 degrees and there is 360 degrees in a circle so 22.5 degrees is the correct answer.

Answer:

5

Step-by-step explanation:

-4-(3+6²)÷13-1²•(-12)=

PEMDAS

parrenthesis:

-4-81÷13-1² x (-12)

exponent:

-4-81÷12 x (-12)

multiplication:

-4-81÷ (-144)

divison:

- 4 - (- 9)

subtraction (Actaully addition +):

= 5

-(- makes plus so -4 + 9 makes 5

Hope this helps, have a good day!! :)

Answer:

A Yes

Step-by-step explanation:

the ratio is 2:1

Answer:

A. yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

a₁ = 10

a₂ = 6

d = a₂  - a₁ = 6 - 10 = -4

n = 16

a₁₆ = a₁ + (n-1)•d = 10 + (16-1)•(-4) = 10 - 60 = -50

[tex]S_{n}=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{16}=\dfrac{10-50}{2}\cdot 16=-40\cdot8=-320[/tex]

Answer:

7/10

Step-by-step explanation:

3/10 + 3/5 - 1/5

Combine like terms

3/10 + 2/5

Get a common denominator of 10

3/10 + 2/5 * 2/2

3/10 +4/10

7/10

Answer:

7/10

Step-by-step explanation:

You want to first get all common denominators, in this case that will be 10.

It is now (3/10)+(6/10)-(2/10)

3+6-2=7

7/10

Answer:

x = 1

Step-by-step explanation:

x² = x

x² / x = 1

x = 1

Check:

1² = 1

Answer:

70 degrees

Step-by-step explanation: this is an equilateral triangle. All of its angles are the same.

Answer:

see below

Step-by-step explanation:

The hypotheses is the if part of the statement ( after the if)

hypotheses:  it is January

The conclusion is the  then part of the statement ( after the then)

conclusion  there is snow

Answer:

The table gives the cost for the number of three-pound bags of clementines. you need to change the number of bags to pounds to be able to get the data for the clementines in units of pounds and cost.

Step-by-step explanation:

each of the bags are three pounds each so 1 bag times 3, 2bags times 3, and then 3bags times 3, hope this answers your question.

The table gives the cost for the number of three pounds bag of clemintines we need to change the number of bags to pounds to get the data or clemintines in units of pounds and cost.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that Clementines are sold in three-pound bags, and navel oranges are sold by the pound

The table represents the cost of three-pound bags of clementines.

Number of Bags           Cost

      1                             $5.00

     2                              $10.00

      3                             $15.00

The equation c = $1.49p represents the cost of the navel oranges, where c is the cost and p is the number of pounds.

The table gives the cost for the number of three pounds bag of clemintines we need to change the number of bags to pounds to get the data or clemintines in units of pounds and cost.

To learn more on Statistics click:

https://brainly.com/question/29093686

#SPJ2

Answer:9/5

Step-by-step explanation:

Answer:

The factorized expression is (-5) × (t - 2.747) ×(t - 1.747)

Step-by-step explanation:

The given expression is -5·t² + 5·t + 24

To factorize the expression by completing the square method, we equate the expression to zero to get;

-5·t² + 5·t + 24 = 0

WE divide by -5 to get;

t² - t - 24/5 = 0

t² - t = 24/5

t² - t + 1/4 = 24/5 + 1/4

(t - 1/2)² = 5.05

t - 1/2 = ±√5.05

t = 1/2 + √5.05, 1/2 - √5.05

The factorized expression becomes;

(t - 1/2 + √5.05) and (t - 1/2 - √5.05)

Which gives;

(t - 2.747) ×(t - 1.747)

The factorized expression is (-5) × (t - 2.747) ×(t - 1.747).

Answer:

16.91176471

Step-by-step explanation:

1725÷102

= 16.91176471

Answer:

H

Step-by-step explanation:

Answer:

Ava's share = $20

Charlotte's share = $16

Step-by-step explanation:

15x + 12x = 36 : multiply each girl's age by same amount and adding gives $36

27x = 36 : add x terms

x = 36 / 27 : divide both sides of equation by 27

x = 4 / 3

Ava's share = 15x = 15 * 4/3 = 20

Charlotte's share = 12x = 12 * 4/3 = 16

Answer:

From scatter plot companies can predict future sales, and what will happen next. To help with this predictions most companies draw a line through the scattered plot called best-fit line. This line should be close to most of the points on the scattered line. Approximately half the point on the top of the line and half on the bottom.In this case the company will ignore the points tat far away from the line.

Scatter plots are useful to compare two variables to see how they relate to one another (if there is any relationship at all). One example could be comparing the temperature outside versus the sales of ice cream. The general trend is that the warmer it gets, the more sales you'll have. So there's an upward trend. We can also say there's a positive correlation as both variables go up together (or go down together).

Contrast this with negative correlation where one variable goes up and the other goes down (eg: hours spent watching tv versus exam score).

Of course, the ice cream example could be too simple and often overused, so it might be better to use something more specific to the company in question. If you picked a company dealing with health/medicine, then you could look at something like height versus weight and see if there's a correlation going on.

Answer:

all real numbers less than or equals to 4

Answer:

-36 = k

Step-by-step explanation:

-3 = k/12

Multiply each side by 12

-3*12 = k/12 *12

-36 = k

Answer: k= -36

Step-by-step explanation:

[tex]-3=\frac{k}{12}[/tex]

multiply both sides by 12

[tex]\frac{12k}{12}=12\left(-3\right)[/tex]

12*(-3)=-36

[tex]\frac{12k}{12}=12\left(-3\right)[/tex]

k=-36

Answer:

[tex]\huge\boxed{-35}[/tex]

Step-by-step explanation:

(-20) + (-15)    [ +(-) = - ]

=> -20-15

=> -35

Answer:

-35

Step-by-step explanation:

a negative plus a negative = negative

negative plus a positive = positive or negative (it depends on which is larger)

negative * negative =  positive

negative * positive= negative

negative-negative= negative

use keep change change

i.e., 8-6 -> 8+-6

change the sign of the middle and the sign of the second term.

Answer:

2

Step-by-step explanation:

Let Ishan’s age equal an unknown quantity we’ll call “x”.

An age 4 times Ishan’s would be 4 times x, written “4x”.

An age 6 years older than Ishan’s would be written “x+6”.

Now, through the magic of algebra, we can write an equation: 4x = x+6 . This means that “four times Ishan’s age is equal to his age plus six.”

The magic continues: you can subtract an”x” from each side of the equation. You can subtract any quantity from either side, but subtracting”x” will leave 6 on the right and “3x” on the left: 3x = 6.

Divide both sides by the same quantity: 3.

This will give you x =2. This indicates Ishan’s age is 2.

Answer:

Ishaan is 2 years old.

Step-by-step explanation:

We can create a systems of equations for this, assuming b is Ben's age and i is Ishaan's age.

[tex]b = 4i[/tex]

[tex]b = i+6[/tex]

Let's solve via substitution.

[tex]4i = i+6[/tex]

Subtract i from both sides:

[tex]3i = 6[/tex]

Divide both sides by 3:

[tex]i = 2[/tex]

So Ishaan is 2 years old. Ben is:

[tex]4(2) = 8[/tex] years old.

Hope this helped!

Answer:

Roughly 20.4%

Step-by-step explanation:

Use the formula of percent of error:

| Actual number - Guess / Actual number | (100)

The actual number is 108 and the guessed number is 86:

| 108 - 86 / 108 | (100)

= | 22/108 | (100)

= | 0.2037037037 | (100)

The vertical lines indicate absolute value.  This means that anything inside of it must be turned into its positive form.  Since it is already positive, just take the signs away:

0.2037037037(100)

≈ 0.204(100)

= 20.4

Turn this into a percent:

20.4%

Martha's percent of error is 20.4%

Please tell me if I was right or not.  I really hope this helps!

Answer:4.2 cups

Step-by-step explanation:

Just do 63 cups, divided by the 15 puppies which equals 4.2 cups! pls mark brainliest

Answer:

4.2 cups

Step-by-step explanation:

I am in the assiment and i just got it right on the assiment

Answer:

She must jog 7 laps in order to meet her goal.

Step-by-step explanation:

A more accurate answer would be that she needs to run 6 1/4 laps to meet her goal. However, because the problem states that she will not be running partial laps, then the number of laps she runs must be a whole number, which in this case works out to be 7 laps.