The go fish game tank contains 30 fish the probability of catching a purple fish is 1/3 the probability of catching a green fish

Answer:

a=80° b=40°

Step-by-step explanation:

a=80 (vertically opposite angles )

a+b+90+150 = 360° ( angle sum property of quadrilateral )

80+b+90+150 = 360

b+ 320 = 360

b= 360-320

b=40°

Answer:

\(\huge \boxed{{10x^2 + 12x \mathrm{\ units^2 }} }\)

Step-by-step explanation:

area of shaded region = area of whole rectangle - area of unshaded region

Area of a rectangle is length × width.

A = 5x(3x+2) - (x(5x-2))

Expand brackets.

A = 15x² + 10x -(5x² - 2x)

Distribute negative sign.

A = 15x² + 10x - 5x² + 2x

Combine like terms.

A = 10x² + 12x

We can conclude that Cab is less than 35/12 µF. Based on the given choices, the correct option is:

C) 5 µF < Cab < 12 µ

To find the equivalent capacitance, Cab, of capacitors connected in series, you can use the formula:

1/Cab = 1/C1 + 1/C2 + 1/C3 + ...

In this case, the known capacitances are 5 µF and 7 µF, and the unknown capacitance is CX. Therefore, we can write the equation as:

1/Cab = 1/5µF + 1/7µF + 1/CX

To determine the relationship between Cab and the given capacitances, we can analyze the equation:

1/Cab = 1/5µF + 1/7µF + 1/CX

Since the given capacitances are positive values, adding positive values together will always result in a larger value. Therefore, we can conclude that:

1/Cab > 1/5µF + 1/7µF

To simplify the expression, we can find a common denominator:

1/Cab > (7 + 5)/(5 * 7)µF

1/Cab > 12/35µF

Taking the reciprocal of both sides:

Cab < 35/12µF

So, we can conclude that Cab is less than 35/12 µF. Based on the given choices, the correct option is:

C) 5 µF < Cab < 12 µF

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The linear equation in slope-intercept form for the velocity of sound as a function of temperature is v = 0.068T + 293.2, where v is the velocity of sound and T is the temperature in degrees Celsius. Using this equation, the velocity of sound at 60°C is 339.6 m/s.

The velocity of sound in dry air increases as the temperature increases. At 40°C, sound travels at a rate of about 355 m/s, and at 49°C, it travels at a rate of about 360 m/s. To write a linear equation in slope-intercept form for the velocity of sound as a function of the temperature, first calculate the slope of the line by finding the difference in velocity divided by the difference in temperature: (360 - 355) / (49 - 40) = 0.068. This slope can be written as the coefficient of the T-term in the equation. To find the y-intercept, plug in the temperature at which the velocity was measured (40°C) and the corresponding velocity (355 m/s) into the equation of the form v = mT + b. Solving for b yields 293.2. Therefore, the linear equation in slope-intercept form is v = 0.068T + 293.2. To find the velocity of sound at 60°C, plug in 60 for T in the equation and solve for v, which yields 339.6 m/s.

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Answer:

10 water stations are needed

Step-by-step explanation:

To get the number of water- station needed, we simply divide the total length of the half marathon by the distance where we can find a water station

mathematically,

that would be 13.1 divided by 1 1/3

= 13.1 divided by 4/3

= 13.1 * 3/4 = 9.825 which is approximately 10

Meters and seconds are the two units of measurement required to describe speed.

A ball freely falling at 20 m/s will in the next second have a speed of 30 m/s.This is because the speed of a freely falling item rises by 9.8 m/s per second owing to gravity's acceleration. The ball begins at a speed of 20 m/s and adds 9.8 m/s to its initial speed after one second, ending in a final speed of 20 + 9.8 = 29.8 m/s (approx. 30 m/s).

Meters and seconds are the two units of measurement required to describe speed. These units are used to calculate the distance travelled by an item as well as the time it takes to traverse that distance. In this scenario, the ball's speed is measured in metres per second (m/s), which is the distance the ball travels in one second.

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If b be a subset of a where |a| = n and |b| = k, then the number of subsets of a whose intersection with b has exactly one element is k × (n-k) C(k-1)

Let's first choose the one element that must be in the intersection of any subset of A with B. Since B has k elements, there are k choices for this element.

Now, we need to choose the remaining (k-1) elements of the subset from A - B, which has n-k elements. There are (n-k) choose (k-1) ways to do this.

Therefore, the total number of subsets of A whose intersection with B has exactly one element is

k × (n-k) choose (k-1)

Alternatively, we can write this as

k × (n-k)C(k-1)

where nCk represents the number of ways to choose k items from a set of size n using combinations.

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Answer:

surface area of cylinder= 2πrh + 2πr²

2×22/7×1×8+2×22/7×1×1

352. + 44

7. 7

= 50.3 + 6.25

= 56.55cm²

Therefore, the solar flux density for mercury after the calculation is 9.12 x 10⁻³ W/m².

The solar flux density also referred to as the solar constant is the total amount of energy derived from the sun per unit area per given unit of time. It is considered to be equal to solar luminosity divided by the surface area of a given sphere that has a radius equivalent to the distance between the respective planet from the sun.

using the formula for finding the solar flux density,

solar flux density =  solar luminosity /(4 x π x distance between mercury and the sun)

solar flux density =  3.865 x \(10^{26}\) /(4 x π x ( 5.791 x \(10^{10}\)))

solar flux density = 9.12 x 10⁻³ W/m²

Therefore, the solar flux density for mercury after the calculation is 9.12 x 10⁻³ W/m².

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Answer:

7.62

Step-by-step explanation:

length* width* height = 3/2*1/2*4=7.62 cm

Answer:

they need $590.1

Step-by-step explanation:

Mrs. Willard already had $475.88 in her savings account. Mr. Willard then received a bonus of $609.00, adding the amounts together would give a total of $1084.88

Since the Willards need $1675.98 for their vacation, subtract $1084.88 from the needed amount, i.e $1675.98-$1084.88

Answer:

591.10

Step-by-step explanation:

hope this helps :D

Answer:

y=(3-x)+(x+2)-(5-x) >>>y=x over the given interval

Answer:

The answer is 5.2. Your welcome :)

Step-by-step explanation:

The equations are solved to w = 0 and z = -2. Option B

From the information given, we have the simultaneous equations as

3w-4z=8

2w+3z=-6

Make w the subject from equation 1

w = 8 + 4z/3

Substitute the value into equation 2, we have that;

2(8 + 4z/3) + 3z = -6

expand the bracket, we get;

16 + 8z/3 + 3z = -6

find the LCM, we have;

16 + 8z + 9z/3 = -6

cross multiply

16 + 17z = - 18

add the values

19z = -34

Make 'z' the subject

z =-2

Substitute the value

3w - 4z = 8

3w = 8 - 8

w = 0

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Answer: there are 3 terms

As per the unitary method, the cost of 8 bottles is $6.48

Unitary Method:

Unitary method is the way of solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

Hawa buys 15 bottles of apple juice at the corner store for a total cost of $12.15.

Here we need to find the if each bottle costs the same amount, how much is 8 bottles of juice.

Let x be the cost of one bottle.

so, based on the unitary method we can written the situation as,

15 bottles = costs $12.15

Therefore, the cost of one bottle is.

x = 12.15/15

x = 0.81

So, the cost of 8 bottle is calculated by multiplying the cost of one bottle with 8,

Then we get,

=> 8 x 0.81

=> 6.48

Therefore, the cost of 8 bottles is $6.48

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Answer:

47 inches and 66 inches

Step-by-step explanation:

took test

Answer:

Hi

Step-by-step explanation:

I am just reply to see if i really understand that problem

Let's assume s the present age of the son, and f the present age of the father.

The age of the son After 10 years is equal to the age of the father before 20 years:

s+10=f+10-20

f=3s

=> s+10=f-10

=> s+10=3s-10

=> 2s=20

=> s=10 and  f=30

Answer:

Allergic to chocolate

Step-by-step explanation:

I don't really eat chocolate that much lol.

Answer:

Well i think i would rather be alergic to chocolate

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

For the given sides to form a triangle.

The sum of any 2 sides must be greater than the third side.

12.2 + 6.8 = 19 > 6.5

12.2 + 6.5 = 18.7 > 6.8

6.8 + 6.5 = 13.3 > 12.2

Thus the 3 given sides form a triangle

Answer:

A=(1/2)(b)(h)

Step-by-step explanation:

The area of a triangle is 1/2(b)(h), so in this case, A=(1/2)(24)(16)=192

By using the concept of supplementary angle, it can be calculated that

The two angles are 47° and 133°

What are supplementary angles?

At first it is important to know about angle.

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

Two angles are said to be supplementary if the sum of the angles is 180°

Let one angle be x

Other angle = 180 - x

The supplement of an angle is 8 less than three times the measure of the angle

By the problem

180 - x = 3x - 8

3x + x = 180 + 8

4x = 188

x = \(\frac{188}{4}\)

x = 47°

Other angle = 180 - 47 = 133°

The two angles are 47° and 133°

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The advantages of the superposition theorem compared to other circuit theorems are its simplicity and modularity in circuit analysis, as well as its applicability to linear circuits.

Superposition theorem is a powerful tool in circuit analysis that allows us to simplify complex circuits and analyze them in a more systematic manner. When compared to other circuit theorems, such as Ohm's Law or Kirchhoff's laws, the superposition theorem offers several advantages. Here are two key advantages of the superposition theorem:

Simplicity and Modularity: One major advantage of the superposition theorem is its simplicity and modular approach to circuit analysis. The theorem states that in a linear circuit with multiple independent sources, the response (current or voltage) across any component can be determined by considering each source individually while the other sources are turned off. This approach allows us to break down complex circuits into simpler sub-circuits and analyze them independently. By solving these individual sub-circuits and then superposing the results, we can determine the overall response of the circuit. This modular nature of the superposition theorem simplifies the analysis process, making it easier to understand and apply.

Applicability to Linear Circuits: Another advantage of the superposition theorem is its applicability to linear circuits. The theorem holds true for circuits that follow the principles of linearity, which means that the circuit components (resistors, capacitors, inductors, etc.) behave proportionally to the applied voltage or current. Linearity is a fundamental characteristic of many practical circuits, making the superposition theorem widely applicable in real-world scenarios. This advantage distinguishes the superposition theorem from other circuit theorems that may have limitations or restrictions on their application, depending on the circuit's characteristics.

It's important to note that the superposition theorem has its limitations as well. It assumes linearity and works only with independent sources, neglecting any nonlinear or dependent sources present in the circuit. Additionally, the superposition theorem can become time-consuming when dealing with a large number of sources. Despite these limitations, the advantages of simplicity and applicability to linear circuits make the superposition theorem a valuable tool in circuit analysis.

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The length of segment GF in the triangle is 8 inches

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

The triangle

On the triangle, we have the following ratio

3 : 6 = 4 : GF

So, we have

GF = 6/3 * 4

Evaluate

GF = 8 inches

Hence, the length is 8 inches

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Answer:

(1,000 * (100 + 12))/100 = 1,120 - 1,000 = 120 turtles/ per year

Step-by-step explanation:

The exponential function which can be use to identify the monthly growth is,

⇒ y = 1000 (1.12)¹²ⁿ

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

That's population of turtles in a lake is estimated at 1,000.

And,  The population projected to increase 12% per year.

Hence, The exponential function which can be use to identify the monthly growth is,

⇒ y = 1000 (1 + 12/100)¹²ⁿ

⇒ y = 1000 (1 + 0.12)¹²ⁿ

⇒ y = 1000 (1.12)¹²ⁿ

Thus, The exponential function which can be use to identify the monthly growth is,

⇒ y = 1000 (1.12)¹²ⁿ

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10k^3 , 6k^3

k^3 ( 10, 6 )

2k^3 (5, 3)

so 2k^3 is the greatest common factor of both the numbers .

Answer:

greatest common factor: 2k³

Step-by-step explanation:

given 10k³ and 6k³

for gcf just simply break them down:

10k³ = 2 * 5 * k * k * k

6k³ =  2 * 3 * k * k * k

-------------------------------------------------------------------------------------------------------------

Analyse both of them and find similarities:

the similarities are: 2 * k * k * k

so the greatest common factor is 2k³

Side 1 + side 2 + side 3

E.g.

2 + 4 + 3 = 9

Have a luvely day!