The aquarium has 10 more red fish than blue fish. 60 percent of the fish are red. How many blue fish are in the aquarium? Show your work. (10 points)​

1. The t-value of the data is 1.833

2. The margin of error is 1.66

3. The confidence interval is between 11.66 to 8.34

From the question given;

sample size = 11

sample mean = 10 inches

standard deviation = 3 inches

1.The t-value of the data with a degree of freedom equal to 10 at 0.05 significance level = 1.833

2. Using the formula below, the margin of error is;

[tex]ME = t * \frac{SD}{\sqrt{n} }[/tex]

Substituting the values into the formula above;

ME = 1.833 * 3/√11

ME = 1.66

3. The confidence interval of the data is;

CI = mean ± ME

where CI is the confidence interval, mean is the sample mean, and ME is the margin of error. In this case, the confidence interval is calculated as follows:

CI = 10 +/- 0.96 = 9.04 to 10.96 inches

CI = 10 ± 1.66 = 11.66 to 8.34

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The Mayan number || :||- € is equivalent to the base-10 number 1021.

To convert a Mayan number to base-10, use the following steps:

In this case, the values of the digits are as follows:

Ones: 1

Twentys: 0

Four-hundreds: 2

Eight-thousands: 1

The place values are as follows:

Ones: 1

Twentys: 20

Four-hundreds: 400

Eight-thousands: 8000

The final value is calculated as follows:

1 × 1 + 0 × 20 + 2 × 400 + 1 × 8000 = 1021

Therefore, the Mayan number || :||- € is equivalent to the base-10 number 1021.

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An additional information that is needed to prove the triangles are congruent by the SAS Postulate is: D. ∠BAC ≅ ∠DAC.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce that ∆BAC is congruent to ∆DAC when the angles A (∠A) are congruent by the reflexive property.

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Answer:
To find the volume of a cone with radius 9 feet and height 4 feet, we can use the formula:

V = (1/3) * π * r^2 * h

Plugging in the values:

V = (1/3) * π * (9^2) * 4

Calculating:

V = (1/3) * π * 81 * 4

V ≈ 108.19 cubic feet

Therefore, the volume of the cone is approximately 108.19 cubic feet (rounded to two decimal places)

The coordinates of the Triangle RST after it is translated 4 units down and 3 units to the left is the option;

R¢(-7, -2), S¢(2, -1), T¢(-1, -9)

A translation transformation is one in which the location of the pre-image is transformed from its initial location to the destination location.

The coordinates of the vertices of the triangle RST are; R(-4, 2), S(5, 3), T(2, -5)

The translation transformation that is applied on the triangle RST includes;

A vertical translation 4 units downwards

An horizontal translation 3 units to the left

The translation transformation is therefore; T₍₋₃, ₋₄₎

Therefore, applying each transformation, we get;

R(-4, 2) ⇒ T₍₋₃, ₋₄₎ ⇒ R¢(-4 -3, 2 - 4) = R¢(-7, -2)

S(5, 3) ⇒ T₍₋₃, ₋₄₎ ⇒S¢(5 - 3, 3 - 4) = S¢(2, -1)

T(2, -5) ⇒ T₍₋₃, ₋₄₎ ⇒ T¢(2 - 3, -5 - 4) = T¢(-1, -9)

The correct option is therefore, the first option

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Two equivalent expressions for the given expression 14(8 - 16x) + 3x are 112 - 221x and 112 - 221x.

Equivalent expression 1:

Expanding the expression 14(8 - 16x) and combining like terms, we get:

112 - 224x + 3x

Simplifying further, we have:

112 - 221x

Equivalent expression 2:

Distributing the coefficient 14 to both terms inside the parentheses, we have:

112 - 224x + 3x

Combining the terms with the same variable, we get:

112 - 221x

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"dom(R) ⊂ UU R" means that the domain of relation R is a subset of the universal set associated with relation R

The notation "dom(R) ⊂ UU R" refers to the domain of a relation R being a subset of the universal set U.

Let me help you to break it down

1. dom(R): This represents the domain of the relation R. The domain of a relation is the set of all elements that appear as the first component in any ordered pair of the relation.

2. ⊂: This symbol indicates a subset relationship, meaning that the set on the left-hand side is a subset of the set on the right-hand side. In this case, "dom(R) ⊂ U" implies that the domain of relation R is a subset of the universal set U.

3. "UU R": The term "UU R" likely represents the universal set associated with relation R. It indicates the set that contains all possible elements that can be related by R.

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Answer:

A)19.0

B)10.0

Step-by-step explanation:

Using [tex]\frac{1}{2} * absin(C)[/tex]

This is used when you have an angle between two sides

Kindly check the attached image for the solution

It will take the truck 9 hours to travel from warehouse A to warehouse B.

To determine the time it takes for the truck to travel from warehouse A at (-4, 8) to warehouse B at (-4, -1), we need to calculate the distance between these two points and then convert it to time using the given unit of 20 miles per hour.

First, let's find the vertical distance between the two points. The y-coordinate of warehouse A is 8, and the y-coordinate of warehouse B is -1. So the vertical distance is 8 - (-1) = 9 units.

Next, we convert the vertical distance to miles. Since each unit represents 20 miles per hour, we multiply the vertical distance by 20: 9 units × 20 miles/unit = 180 miles.

Now, we can calculate the time it takes to travel this distance. We divide the distance by the speed of the truck, which is 20 miles per hour: 180 miles / 20 miles per hour = 9 hours.

Therefore, it will take the truck 9 hours to travel from warehouse A to warehouse B.

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Answer: "The pyramid and the cone have the same volume despite their different shapes."

Step-by-step explanation: If a pyramid and a cone are both 10 centimeters tall and have the same volume, then the statement that can be made is:

"The pyramid and the cone have the same volume despite their different shapes."

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Answer:

Step-by-step explanation:

Answer:

Part A: The actual measurement of the piece of wood could be between 9.65 and 9.75 inches.

Part B: The measurement has three significant digits.

Step-by-step explanation:

Significant digits are the digits in a number that carry meaning in terms of the precision or accuracy of the measurement. In this case, the number 9.7 has three significant digits, which means that the measurement is accurate to the tenths place.

The sequence of transformations that maps triangle ABC onto triangle A'B'C' is a translation by (+8, -6) followed by a reflection across the y-axis.

To determine the sequence of transformations that maps triangle ABC onto triangle A'B'C', let's analyze the given coordinate points.

Triangle ABC:

A (-4, 4)

B (-8, 2)

C (-6, -6)

Triangle A'B'C':

A' (4, -2)

B' (2, 2)

C' (6, 0)

By comparing the corresponding vertices, we can identify the transformations:

Translation:

To transform A to A', we can observe that A' is obtained by moving 8 units to the right and 6 units downwards from A. Therefore, the first transformation is a translation by (+8, -6).

Reflection:

Next, we notice that B' is the reflection of B across the y-axis. Thus, the second transformation is a reflection about the y-axis.

Therefore, the sequence of transformations that maps triangle ABC onto triangle A'B'C' is a translation by (+8, -6) followed by a reflection across the y-axis.

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The voltage drop across resistor R₃ is determined as 237.9 V.

The total current flowing in the circuit is calculated by applying Ohm's law as shown below.

V = IR

I = V / R

where;

Since the circuit is in series connection, the total resistance is calculated as follows;

R = R₁ + R₂ + R₃

R = 76 ohms + 61 ohms + 30 ohms

R = 167 ohms

The current flowing in each circuit component is calculated as;

I = V/R

I = 1325 V / 167Ω

I = 7.93 A

The voltage drop across R₃ is calculated as follows;

V₃ = IR₃

V₃ = 7.93 x 30

V₃ = 237.9 V

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The complete question is below:

This cirucit is in series. Determine the voltage dropped on R3, given:

ET = 1325 V, R1 = 76 Ω, R2 = 61 Ω, R3 = 30 Ω, and R4 = 30 Ω

Answer: its D! not 8!!!

Step-by-step explanation:

The length of the segment shown in the graph is 10 units

The endpoints on the line segment are : (2, - 1) and (-4,7)

The Length of a line segment can obtained using the relation :

Length = √(x2 - x1)² + (y2 - y1)²

Here,

x2 = - 4, x1 = 2, y2 = 7, y1 = - 1

Length of segment = √((-4) - 2)² + (7 - (-1))²

Length of segment = √(-6)² + (8)²

Length of segment = √36 + 64

Length of segment = √100 = 10 units

Therefore, the length of the segment on the graph shown is 10 units.

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Answer:

[tex]\huge\boxed{\sf r = 5}[/tex]

Step-by-step explanation:

Given that,

7q + 35 = 7q + 7r

7q - 7q + 35 = 7q - 7q + 7r

35 = 7r

35/7 = r

5 = r

OR

[tex]\rule[225]{225}{2}[/tex]

Answer:

r = 5

Step-by-step explanation:

Given statement,

→ 7(q + 5) is equivalent to (q + r)7.

Forming the equation,

→ 7(q + 5) = 7(q + r)

Now we have to,

→ Find the required value of r.

Then the value of r will be,

→ 7(q + 5) = 7(q + r)

Applying Distributive property:

→ 7(q) + 7(5) = 7(q) + 7(r)

→ 7q + 35 = 7q + 7r

Cancelling 7q from both sides:

→ 35 = 7r

→ 7r = 35

Dividing the RHS with number 7:

→ r = 35/7

→ [ r = 5 ]

Therefore, the value of r is 5.

The area of the shaded region is  104 cm²

First, we need to know that the area of a circle is calculated using the formula;

A = πr²

Such that the parameters of the formula are;

First, let us find the area of the small circle

Area = 3.14 × 4²

Find the square value and multiply, we have;

Area = 50.24cm²

Area of the large circle = 3.14 × 7²

Find the square value and multiply

Area = 153. 86cm²

Area of the shaded region = Area of large circle - area of small circle

= 153.86 - 50.24

= 104 cm²

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Answer:

The sum of 33, 78, 10, 98, and 76 is 295.

Answer:

295

Step-by-step explanation:

add the numbers by using the addiction sign

The velocity represented by vector AC of Michelle's canoe is approximately option C. 11.2 miles per hour.

To determine the velocity, represented by vector AC, of Michelle's canoe, use the concept of vector addition.

Break down the motion into its components:

1. Paddling due east at 10 miles per hour: This motion can be represented by a vector pointing in the positive x-direction with a magnitude of 10 mph.

2. Wind blowing due south at 5 miles per hour: This motion can be represented by a vector pointing in the negative y-direction with a magnitude of 5 mph.

To find the resultant velocity, add these two vectors. Using the Pythagorean theorem, calculate the magnitude of the resultant velocity:

AC² = AB² + BC²

AB (paddling east) = 10 mph

BC (wind blowing south) = -5 mph (negative sign due to opposite direction)

AC² = (10 mph)² + (-5 mph)²

AC² = 100 mph² + 25 mph²

AC² = 125 mph²

Taking the square root of both sides:

AC ≈ √(125) mph

AC ≈ 11.2 mph (rounded to the nearest tenth)

Therefore, the velocity represented by vector AC of Michelle's canoe is approximately 11.2 miles per hour.

The correct answer is option C: 11.2 miles per hour.

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Answer:

Step-by-step explanation:

32 60 68

The mean weekly expense, after correcting the incorrectly recorded week, is $81.25.

Given that Taylor recorded the past 16 weeks' expenses, excluding the incorrect recording of $90 as $38, we have 15 correct expense values.

Sum of correct expenses = $83.20 * 15 = $1248

Now we need to include the corrected expense of $90 instead of $38.

New sum of expenses = $1248 - $38 (incorrectly recorded) + $90 (corrected) = $1300

Finally, we calculate the mean by dividing the new sum by the total number of weeks, which is 16.

Mean weekly expense = $1300 / 16 = $81.25

Therefore, the mean weekly expense, after correcting the incorrect recording, is $81.25.

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Appling the tangent of circle properties, the length of RS is solved to be

C. 13 in

To find the length of the tangent named RS, we applied the tangent of a circle property which says that the length of tangents to a particular point are equal

This leads to the mathematical equation represented below

SR = 7 in + 6 in

SR = 13 in

thus we can say that length of the tangent SR = 13 in

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y=2/3x-4 is the equation of the line where 2/3 is the slope.

We have to find the equation of line which is passing through points (0, -4) and (3, -2).

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁.

Slope = -2+4/3-0

=2/3

Now let us find the y intercept.

-4=2/3(0)+b

b=-4

The equation of line is y=2/3x-4.

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The total area of the quadrilateral DEFG is determined as 154 cm² .

option A.

The total area of the quadrilateral DEFG is calculated by applying the following method.

Consider triangle GDE in the quadrilateral;

base of the triangle = 16 cm

height of the triangle = 8 cm

Area of the triangle GDE = ¹/₂ x base x height

Area of the triangle GDE = ¹/₂ x 16 cm x 8 cm

Area of the triangle GDE = 64 cm²

Consider triangle GEF in the quadrilateral;

base of the triangle = 18 cm

height of the triangle = 10 cm

Area of the triangle GEF = ¹/₂ x base x height

Area of the triangle GEF = ¹/₂ x 18 cm x 10 cm

Area of the triangle GEF = 90 cm²

The total area of the quadrilateral DEFG is calculated as;

Area =  64 cm² +  90 cm²

Area = 154 cm²

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Answer:

Length of third side = 30 inches

Step-by-step explanation:

We will need a system of equations to find the length of the third side.

First equation:

We know the perimeter of a triangle is simply the sum of its sides.

Thus, since the perimeter is 45, our first equation is x + x + y = 45, which simplifies to 2x + y = 45.

Second equation:

Since we're told that the length of the third side is twice as long as the sum of the congruent sides, our second equation is y = 2(x + x), which simplifies to y = 2(2x) and then finally y = 4x

Method:  Substitution.

We can first solve for x (length of one of the congruent sides) by substituting y = 4x for y in 2x + y = 45:

2x + 4x = 45

6x = 45

x = 7.5

Find y:

Now we can find y (length of the third side) by plugging in 7.5 for x in y = 4x:

y = 4(7.5)

y = 30

Thus, the length of the third side is 30 inches.

Optional Step to check validity of answers.

First equation:  Check that the sum of 7.5, 7.5, and 30 = 45

7.5 + 7.5 + 30 = 45

15 + 30 = 45

45 = 45

Second equation:  Check that 30 is twice the sum of 7.5 + 7.5

30 = 2(7.5 + 7.5)

30 = 2(15)

30 = 30

Thus, our answers are correct and we've correctly determined the length of the third side of the triangle in inches.

To solve the equations:

O + O + O = 30

1 - 3 - 5 - 7

9 - 11 -

15

We can start by simplifying the second equation:

1 - 3 - 5 - 7 = -14

9 - 11 - x = -14

To find the value of x, we can solve the equation:

-11 - x = -14

Adding 11 to both sides of the equation:

-11 + 11 - x = -14 + 11

Simplifying:

-x = -3

Multiplying both sides by -1:

(-1) * (-x) = (-1) * (-3)

x = 3

Now, substituting the value of x back into the second equation:

9 - 11 - 3 = -14

-5 - 3 = -14

-8 = -14

This is not a true statement. Therefore, the values provided do not satisfy the equations given.

y = -3x + 2 is the equation of the line, in slope-intercept form, with the following information.

Thus, The most "popular" type of a straight line is one with a slope-intercept. Due of its simplicity, this is helpful to a lot of kids.

The slope and y-intercept of the straight line can be easily determined or read off from this form, making it possible to describe its properties without having access to the graph.

You may learn how to determine the equation of a line from any two points that this line passes through using the slope intercept form calculator.

Continue reading to find out what a linear equation's slope intercept form is, how to calculate a line's equation, and the significance of the slope intercept form equation in practical applications.

Thus, y = -3x + 2 is the equation of the line, in slope-intercept form, with the following information.

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