A competition to catch the most rainbow trout on Lake Rainbow pitched the men against the ladies. 16 men and 12 women participated. Each participant had a total of 15 attempts before they retired from the competition. It was predicted that the men would have a 9% chance of catching a rainbow trout at each attempt. One participant's experience resulted in 3 successful catches. The probability that this participant was a woman is 40%. Find the probability that a participant successfully catches 3 rainbow trout, given that the participant was a woman.

The area of the logo using the length and the width is 162 cm²

Length of logo = 16 cm

Width of logo = 12 cm

Area of logo = length × width

= 16 cm × 12 cm

= 192 cm²

Therefore, the area of the logo using the length and the width is 162 cm²

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The sample space of event A would be {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

An experimenter does some random experiments which have a fixed set of outputs. That set of all possible outputs of that experiment is called sample space.

Using two six-sided number cubes, each labeled with the numbers 1 through 6.

Event A is defined by rolling a sum greater than 8.

Then the sample space of event A would be;

{(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

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Answer:

{(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

proof in pic

Hey there!

ASSUMING:

p = 2l + 2w

IF SO:

• We already have our perimeter (p) & our width (w), now you have to find our length (l)

160 = 2l + 2(34)

CONVERT TO:

2l + 2(34) = 160

SIMPLIFY IT:

2l + 68 = 160

SUBTRACT 68 to BOTH SIDES:

2l + 68 - 68 = 160 - 68

SIMPLIFY IT:

2l = 160 - 68

2l = 92

DIVIDE 2 to BOTH SIDES:

2l/2 = 92/2

SIMPLIFY IT:

l = 92/2

l = 46

Therefore, your answer should be:

l = 46

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

The diver's position in feet (depth) when she swims with dolphins is -83 feet.

Step-by-step explanation:

First highlight the important information from the question.

A diver sits on a boat at the surface of the ocean preparing to dive. She dives in and descends to -128 feet. After a few minutes, she ascends 45 feet to swim with a pod of dolphins that has appeared. What integer represents the diver's position in feet (depth) when she swims with the dolphins?

So, first she descends -128 feet, then she ascends 45 feet to swim with dolphins. So, now that we have the important information highlighted we can solve the problem.

-128+45=-83.

The diver's position in feet (depth) when she swims with dolphins is -83 feet.

Hope this helps!

If not, I am sorry.

The slope of the given equation of the straight line is - 5/4.

We know that the direction of a line is defined by its slope. The slope is calculated by dividing the difference between the y-coordinates of two points on a line by the difference between their x-coordinates.

Here the equation of the line is

y = - (5/4)x - 1.

At x = 0, y = -(5/4) × 0 - 1 = -1

and at x = 4, y = -(5/4) × 4 - 1 = - 5 - 1 = -6

Now the slope = (-6 - (-1))/(4 - 0) = (-6 + 1)/4 = - 5/4

Therefore the slope of the given equation of the straight line is - 5/4.

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Answer:

[tex]\sf y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]

Step-by-step explanation:

Given equation: -3x + 7y = 21

Slope-Intercept Form: y = mx + b -

where:

Note: parallel lines have the same slope.

1. Rewrite the given equation in slope-intercept form:

[tex]\sf -3x + 7y = 21\ \textsf{[add 3x to both sides]}\\\\-3x + 3x + 7y = 21 + 3x\\\\7y = 3x + 21\ \textsf{[divide both sides by 7]}\\\\\dfrac{7y}{7}=\dfrac{3x+21}{7}\\\\\implies y=\dfrac{3}{7}x+3[/tex]

Here, this equation has a slope of ³⁄₇ and a y-intercept of 3.

2. Find the equation of the parallel line:

substitute the point (4, 9) into the equation to find the value of b

[tex]\sf y=\dfrac{3}{7}x+b\\\\9=\dfrac{3}{7}(4)+b\\\\9=\dfrac{12}{7}+b\\\\\dfrac{63}{7}-\dfrac{12}{7}=\dfrac{12}{7}-\dfrac{12}{7}+b\\\\\dfrac{51}{7}=b[/tex]

[tex]\sf \textsf{Equation:}\ y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]

3. Check your work:

[tex]\sf y=\dfrac{3}{7}x+\dfrac{51}{7}\\\\9=\dfrac{3}{7}(4)+\dfrac{51}{7}\\\\9=\dfrac{12}{7}+\dfrac{51}{7}\\\\9=\dfrac{63}{7}\\\\9=9\ \checkmark[/tex]

[tex]\sf \textsf{Therefore, the equation of the parallel line is:}\ y=\dfrac{3}{7}x+\dfrac{51}{7}[/tex]

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Answer:

[tex]\sf y=\dfrac{3}{7} x+\dfrac{51}{7}[/tex]

Step-by-step explanation:

First, write the given equation in slope-intercept form. That is, you can make y the subject in the given equation.

Slope intercept form

y = mx + c

Here,

m = slope

c = y-intercept

Let us write the given equation in slope-intercept form.

− 3x + 7y = 21

Add 3x to both sides.

7y = 3x + 21

Divide both sides by 7.

[tex]\sf y=\dfrac{3}{7}x +\dfrac{21}{7} \\\\y=\dfrac{3}{7}x +3[/tex]

We know that the slopes of parallel lines are equal. Therefore, the slope(m) of the new line is 3/7.

The new line is going through ( 4, 9 ). Using that, let us find the value of c (y-intercept), by substituting the values of m, y, and x.

( 4, 9 ) → ( x , y )

m → 3/7

Let us find the value of c

[tex]\sf y = mx+c\\\\9 =\dfrac{3}{7}*4+c\\\\ 9=\dfrac{12}{7}+c\\\\ 9-\dfrac{12}{7}=c\\\\\dfrac{63-12}{7} =c\\\\\dfrac{51}{7} =c[/tex]

And now let us write the equation of the new line.

[tex]\sf y =mx+c\\\\\sf y=\dfrac{3}{7} x+\dfrac{51}{7}[/tex]

Answer:

In the given Triangle problem, the three options are:

1.  m∠5 + m∠6 = 180°

2. ∠2+ ∠3 = ∠6

3. m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

Concept: Consider Δ ABC with Exterior angles ∠1, ∠4 and ∠6.

Use the Exterior angle Property of Triangle which says that an exterior angle of a triangle is equal to the sum of the opposite interior angles.

For Exterior angle ∠1 we have:

∠1 = ∠5 + ∠3

Similarly, for Exterior ∠4 we have:

∠4 = ∠5 + ∠2

Similarly, for Exterior ∠6 we have:

∠6 = ∠2 + ∠3

Now, use the Triangle Sum Property which states that in a triangle sum of the measures of angles is equal to 180°

m∠2 + m∠3 + m∠5 = 180°

Linear Pair:

The measure of a straight angle is 180°, so a linear pair of angles must add up to 180°.

m∠5 + m∠6 = 180°

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Answer:

[tex]\huge\boxed{\sf AB = 8.86 \ cm}[/tex]

Step-by-step explanation:

θ = 41°

Hypotenuse = BC = 13.5 cm

opposite = AB = ?

We will use the trigonometric ratio of sin.

[tex]\displaystyle sin \ \theta = \frac{opposite }{hypotenuse} \\\\sin \ 41=\frac{AB}{13.5} \\\\0.656 = \frac{AB}{13.5} \\\\0.656 \times 13.5 = AB\\\\8.86 \ cm = AB\\\\\boxed{ AB = 8.86 \ cm}\\\\\rule[225]{225}{2}[/tex]

0.90 nearest tenth is 9 since there is no other number to help round it over.

Answer:

5.1

Step-by-step explanation:

A rational number is any number that can be written as a fraction, or is a decimal that terminates or repeats.

Answer:

D. n=3

Step-by-step explanation:

8-2n-6n= –16

Take 8 to the other side

-2n-6n= -16-8

Solve them

-8n = -24

Take -8 to the other side

[tex]n \: = \frac{ - 24}{ - 8} [/tex]

n = 3

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{8 - 2n - 6n = -16}[/tex]

[tex]\huge\textbf{Solving for the answer:}[/tex]

[tex]\mathbf{8 - 2n - 6n = -16}[/tex]

[tex]\huge\textbf{Combine the like terms:}[/tex]

[tex]\mathbf{(-2n - 6n) + 8 = -16}[/tex]

[tex]\mathbf{-2n - 6n + 8 = -16}[/tex]

[tex]\mathbf{-8n + 8 = -16}[/tex]

[tex]\huge\textbf{Subtract \boxed{\bf 8} to both sides:}[/tex]

[tex]\mathbf{-8n + 8 - 8 = -16 - 8}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{-8n = -16 - 8}[/tex]

[tex]\mathbf{-8n = -24}[/tex]

[tex]\huge\textbf{Divide \boxed{\bf -8} to both sides:}[/tex]

[tex]\mathbf{\dfrac{-8n}{-8} = \dfrac{-24}{-8}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{n = \dfrac{-24}{-8}}[/tex]

[tex]\mathbf{n = -24 \div -8}[/tex]

[tex]\mathbf{n = 3}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\textsf{Option D. \boxed{\frak{n = 3}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

y=2x+1

Step-by-step explanation:

Answer:

[tex]12x^9+15x^8 -8x^6-10x^5[/tex]

Step-by-step explanation:

[tex]~~(x^4)(3x^3 -2)(4x^2 +5x)\\\\=(3x^7-2x^4)(4x^2 +5x)\\\\=12x^9+15x^8 -8x^6-10x^5[/tex]

Therefore, [tex]\frac{8}{7}= 1.14[/tex] cannot represent the probability of an event. So, option C is correct.

We need to identify which of the given option cannot represent the probability of an event.

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.

By simply dividing the favourable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favourable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

Now, [tex]\frac{1}{14} =0.0714, \frac{8}{7}= 1.14[/tex] and [tex]\frac{20}{21}=0.952[/tex].

Therefore, [tex]\frac{8}{7}= 1.14[/tex] cannot represent the probability of an event. So, option C is correct.

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Answer:

Divide the shape in two pieces:

A rectangle and a triangle

Find area of rectangle:

A=length*width=5*4=20m^2

Find area of triangle:

base of triangle=5-2=3m

height of triangle=8-4=4m

Area=(1/2)*base*height

=(1/2)(4)(3)=6m^2

Total area=6+20=26m^2

Hope it helps!

The graph goes upwards on the left side and downwards on the right side, so the correct option is the first one.

We have the function:

[tex]y = -9*x^3 + 5*x^2 -2x[/tex]

This is a cubic polynomial with a negative leading coefficient.

So, when x takes large negative values, because the leading coefficient is negative, y will take large positive values.

And when x takes large positive values, because the leading coefficient is negative, y will take large negative values.

So the nature is:

The graph goes upwards on the left side and downwards on the right side. The correct option is the first one.

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Step-by-step explanation:

in general we would need a probabilty table or a probability calculator service on the internet.

but in this case we know.

the man value is 64. and the standard deviation is 6.

so, one standard deviation +/- interval from the mean value is 70 and 58.

and the interval of 2 standard deviations from the mean value is 76 and 52.

and 64 and 76 are exactly the limits we are asked for.

so, remember the normal distribution rule :

68% are within 1 standard deviation.

95% are within 2 standard deviations.

99.7% are within 3 standard deviations.

and 50% are below (and also above) the mean value.

so, we know, 50% of the 350 (= 175) students scored below 64.

95% of the students scored between 76 and 52. as there are 5% left, half of these 5% (= 2.5%) scored even below 52).

so, 95% + 2.5% = 97.5% of the 350 (= 341.25) students scored below 76.

therefore, the number of students that scored between 64 and 76 is

341.25 - 175 = 166.25 ≈ 166

Answer:

9 men

Step-by-step explanation:

If 6 men are required to complete a job in 8, than 9 men would be required for a 12 day job.

12-8=4 which is half of 8

Half of 6 is 3

6+3=9

Answer:

4 men

Step-by-step explanation:

• Let x be the number of men needed to do the work I need 12 days.

•• it’s clear that the two variables (number of men and number of hours are in inverse proportion)

•• Which means their product is always equal to a constant.

Therefore

12 × x = 6 × 8 = 48

Then

x = 48 ÷ 12

  = 4

Step-by-step explanation:

F1/A1 = F2/A2

10/2=F2/4

5=F2/4

F2=5x4

F2=20

Answer: The answer for this problem is all real numbers or R.

Step-by-step explanation: In order to solve first you must deal with what's inside the parenthesis.

[tex]8(4x+2)=8*4x + 8*2= 32x +16[/tex]

Now that the parenthesis is out of the picture, now proceed to subtract the 16 that was outside of the parenthesis.

[tex]32x+16-16=32x[/tex]

You should then have an equation set up like so.

32x = 32x

Now you need to move one of the 32x's to the other side of the equation.

[tex]32x-32x=0[/tex]

Your final equation should be.

0 = 0

So, all real numbers (R) will work for this equation.

The positive linear correlation is present in the scatter plot option first “positive” is correct.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\[/tex]

[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

We have given a scatter plot in the picture.

As we can see in the scatter plot the dots are not so close that the correlation between x and y will be weak.

If we draw a line of best fit the slope of the line will be positive, the correlation will be positive.

Thus, the positive linear correlation is present in the scatter plot option first “positive” is correct.

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Answer:

x = 14.02 units

Step-by-step explanation:

Finding unknown value using Pythagorean theorem:

 This is an isosceles trapezium.  The two perpendiculars  divide the trapezium into two congruent triangles and a rectangle. Let the base of the triangle by 'y'. We can find the value of 'y' using Pythagorean theorem.      

In ΔABC,

                AC² = AB² + BC²

                   19² = 17 ² + y ²

                 361  = 289 + y ²

        361 - 289  = y ²

                      y ² = 72

                      y =√72

                      y = 8.49

x = 31 - 8.49 - 8.49

x = 14.02

The value of the 6 is 3.

If you write 1 in word then you will write one and if you count the letter it will give you 3

Similarly, if you write the numbers 2,3,4,5 in word and count the number you will get 3,5,4,4 respectively.

counting Letters provides a perfect way to introduce number words to beginning readers, as well as discuss the concepts of letters and words.

So, if you write 6 in words you will write six and on counting the letter you will get 3.

Hence, 6 = 3 ans.

Therefore the value of the 6 is 3.

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Answer:

£69

Step-by-step explanation:

Given information:

Cost of buying a dress and shoes:

⇒ £50 + £43 = £93

Discount:

⇒ 1/3 of £93 = 1/3 × 93 = £31

Cost of goods after discount is applied:

⇒ £93 - £31 = £62

Addition of shipping and handling:

⇒ £62 + £7 = £69

Therefore, Ruth will pay £69 if she buys a dress and shoes.

Answer:

Step-by-step explanation:

a=-110

d=-102-(-110)=-102+110=8

let n be the number of terms.

74=-110+(n-1)×8

74=-110+8n-8

74+118=8n

192=8n

n=192/8=24

[tex]s=\frac{n}{2} [2a+(n-1)d]\\s=\frac{24}{2} [2(-110)+(24-1)\times8]\\=12[-220+184]\\=12(-36)\\=-432[/tex]

Answer:

g(-0.0001) = -9

g(0.0001) = -1

g(0) = -1

g(9) undefined

Step-by-step explanation:

g(9) undefined .because the graph have an empty circle

at (9 , 0) which means g is not defined at 9.