a phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phylum. a simple random sample of 50 alga is obtained and each alga is categorized as either being a cyanobacterium or not. the researcher found that 38 samples were, in fact, cyanobacteria. without relying on any previous knowledge, the researcher wanted to estimate the proportion of algae that were cyanobacteria with a margin of error of at most 0.01 in a 99% confidence interval. how large a sample size would be required?

The equation of the line that is parallel to the line y = -2x + 1 and passing through (-6, -7) will be y = -2x - 13.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The slope of the parallel line will remain the same. Then the equation of the line that is parallel to the line y = -2x + 1 will be given as,

y = -2x + c

The equation passes through (-3, -7), then the value of the variable 'c' is given as,

- 7 = -2(-3) + c

-7 = 6 + c

c = - 13

Then the equation of the line that is parallel to the line y = -2x + 1 and passing through (-6, -7) will be y = -2x - 13.

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Answer:

Step-by-step explanation:

a + b)^6 will have 7 terms so you want row 6 of the triangle 1 6 15 20 15 6 1

so (a + b)^6 = a^6 + 6a^(5)b + 15a^(4)b^2 + 20a^(3)b^3 + 15a^(2)b^4 + 6ab^5 + b^6

given a = d and b = -5y

∴ (d − 5y)^6 = d^6 + 6d^(5)(-5y) + 15d^(4)(-5y)^2 + 20d^(3)(-5y)^3 + 15d^(2)(-5y)^4 +

The value x from given triangle FGH of x is 11.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

From the given figure, ∠G=2x+8, ∠H=65° and ∠JFG=9x-4.

Here, ∠JFG=∠G+∠H

⇒ 9x-4=2x+8+65

⇒ 9x-2x=73+4

⇒ 7x=77

⇒ x=11

Hence, the value of x is 11.

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The translation from the triangle ABC to triangle A'B'C' is 3 units right and 2 units up.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

Given that,

The coordinates of triangle ABC are A(-3, 1), B(-1, 2) and C(1, 1)

The coordinates of triangle A'B'C' are A'(0, 3), B'(2, 4) and (4, 3).

When the shape is moved towards the right by k units, then replace x with x + k.

When the shape is moved up by k units, then replace y with y + k.

A(-3, 1)→A'(-3+3, 1+2)

B(-1, 2)→B'(-1+3, 2+2)

C(1, 1)→C'(1+3, 1+2)

Therefore, the translation is 3 units right and 2 units up.

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Answer:6 3/10

Step-by-step explanation:

use Desmos calculator

Juan sells 1148 more surfboards than beach toys and sells 1435 fewer bathing suits than beach toys.

As of the mentioned data, Juan has three different surf shops at Sunny Beach. Where he sold 12,195 surfboards, 9,612 bathing suits, and 11,047 beach toys.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

here,
The difference in beach toys and surfboard sell = 12,195 - 11,047 = 1148
Differences in beach toys and bathing suit seel = 9612 - 11047 = -1435

Thus, Juan sells 1148 more surfboards than beach toys and sells 1435 fewer bathing suits than beach toys.

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constructing cones a right triangle whose hypotenuse is 23 m long is revolved about one of its legs to generate a right circular cone. radius: 11.5 m height: 23 m volume: 1650.6 m³

The hypotenuse of the triangle is 23 m. This means that the two sides are 11.5 m and 11.5 m. This gives us the radius of the cone.

The height of the cone is the same as the hypotenuse, so the height is 23 m.

The volume of a right circular cone can be calculated using the following formula: V = (πr²h)/3. In this case, the radius is 11.5 m, the height is 23 m, and π = 3.14. Plugging these values into the formula, we get a volume of 1650.6 m³.

V = (πr²h)/3

V = (3.14 × 11.5² × 23)/3

V = 1650.6 m³

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Answer:

x= 24 − 9y

x= 3/2 − 3y/2

Step-by-step explanation:

In 2021, 65.6 percent of mothers with children under age 6 participated in the labor force

Percentages are fundamentally fractions with 100 as the denominator. To show that a number is a percentage, the percent symbol (%) is placed next to it. For instance, if you answered 45 out of 100 questions on a test accurately (45/100), you would have gotten a 45% mark.

According to the given information

In 2021, 65.6 percent of mothers with children under age 6 participated in the labor force compared with 75.5 percent of mothers whose youngest child was age 6 to 17.

In 2021, 65.6 percent of mothers with children under age 6 participated in the labor force

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Answer:

The answer is 2/3x - y = 15

Step-by-step explanation:

Answer: A

Step-by-step explanation:

adding two circles to the left side would result in square triangle circle circle and if you add a square to the right it would be circle circle triangle square thus balancing it

The maximum period of time they could reserve the meeting space is 9 hours.

Mathematical expressions with the symbols > and are known as inequality. Finding a range, or ranges within ranges, of values that an unknown x can have while still satisfying the inequality is referred to as "solving" an inequality. In this lesson, inequalities are resolved using graphs and algebra.

An algebraic inequality expression is a mathematical statement that uses the it as a sign to connect an expression to a value, a variable, or another expression. One type of variable inequalities can have solutions that can be graphed either in a coordinate plane or on a number line.

Inequality expression is 31 + 5.9*t < 84.10.

To understand it, collect all constant on the right side:

5.9*t < 84.10 - 31 = 53.10,

Hence, t < 53.10 % 5.9 = 9 hours.

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Correct Question:

To rent a certain meeting room, a college charges a reservation fee of $31 and an additional fee of $5.90 per hour. The chemistry club wants to spend less than $84.10 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality for t.

To dilate a rectangle by 2 , multiplied by the scale factor with every coordinates of rectangle

Assume that, the origin (0, 0) be the center of dilation in the coordinate plane.

Let ABCD be a Rectangle in the coordinate plane. The points in the coordinate planes are A(-2, 2), B(3, 2), C(3, -2), D(-2, -2)

We have to dilate by scale factor 2, then every coordinate point of the original triangle will multiplied by the scale factor

Coordinates of new rectangles : A'(-4,4) , B'( 6, 4) ,C(6, -4) and D'(-4,  -4)

Therefore, When we dilate a rectangle by scale factor 2 ,

The dilated triangle will be A’B’C’D’ and the coordinate points obtained are  A'(-4,4) , B'( 6, 4) ,C(6, -4) and D'(-4,  -4)

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The best approximation for the area of this circle with a radius of 8in is 201.0 in².

A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius). The area, a circle occupies in a two-dimensional plane is known as the area of the circle. Therefore, the area that a circle with radius r encloses is πr².

Given the radius r of the circle is 8 in. Then, the area is,

A = 3.14×(8 in)² =200.96 in²=201.0 in²

The answer is 201.0 in² and the correct option is option c.

The complete question is -

What is the best approximation for the area of this circle? Circle with radius labeled 8 in. Use 3.14 to approximate pi.  a) 25.1 in² b) 50.2 in² c) 201.0 in² d) 803.8 in²

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Answer:

A strong positive association

Step-by-step explanation:

A perfect fit for a positive line would be 1.  A perfect fit for a negative line would be -1.

The scale goes from 1 tp -1.  

.86 is pretty close to 1.

Answer:

a = −1 / 2 b^3 + 1 / 2 bh

Step-by-step explanation:

1 )

h = 2a / b^1 + b^2

2 ) Multiply both sides by b.

bh = b^3 + 2a

3 ) Flip the equation.

b^3 + 2a = bh

4 ) Add -b^3 to both sides.

b^3 + 2a + −b^3 = bh + −b^3

2a = −b^3 + bh

5 ) Divide both sides by 2.

2a / 2 = −b^3 + bh / 2

a = −1 / 2 b^3 + 1 / 2 bh

Hope this helps! :)

The unknown wavelength of a light with m= 4 bright fring overlaps m = 3 bright orange fringe and used in a double slit is 450 nm.

Double Slit experiment:

In modern physics, the double-slit experiment shows that light and matter can exhibit properties of both classically defined waves and particles.

Furthermore, it demonstrates the fundamental stochastic nature of quantum mechanical phenomena.

Formula ,

λ = x.d/n.L

where , λ = wavelength of light used (nm)

x = distance from central fringe (m)

d = distance between the slits (m)

n = the order of the fringe

L = length from slits to the viewing screen (m)

thus, taking ratios for the two waves: let w = unknown wavelength

600/w = 4/3 (as other factors are same for both)

thus, w = 450 nm

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Complete questions :

A double slit is illuminated simultaneously with light of wavelength 700 nm and light of an unknown wavelength. The m = 4 bright fringe of the unknown wavelength overlaps the m = 3 bright orange fringe What is the unknown wavelength? Express your answer to three significant figures and include the appropriate units.

The equation of the line passing through the points (0, -6) and (7, 4) in slope-intercept form is y = [tex]\frac{10}{7}[/tex]x - 6.

Slope of a line is defined as the tangent of the angle that the line makes with X axis.

Slope, usually denoted by 'm' of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by,

m = (y₂ - y₁) / (x₂ - x₁)

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

Here, we have two points (0, -6) and (7, 4).

m = (4 - -6) / (7 - 0) = 10/7

y intercept is the y coordinate of the point where the line touches with the Y axis. x coordinate will be zero there.

We already have such point (0, -6).

So b = -6

Substituting these in slope-intercept form,

y =  [tex]\frac{10}{7}[/tex]x - 6

Hence, the equation of the given line in slope intercept form is y = [tex]\frac{10}{7}[/tex]x - 6.

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The ratio is 7:4 for the line joining the points (- 5 1) and (2 3)

In mathematics, a ratio shows how many times one number is represented by another. TA ratio can have quantities of any kind, such as counts of persons or objects, measurements of lengths, weights, or times, etc. Both numbers must be positive in the vast majority of situations.

We can calculate the ratio by subtracting the x-values and y-values of the given points:

(2 + 5) : (3 - 1)

= 7 : 4

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Answer:

option 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0-(-2)}{4-0}[/tex] = [tex]\frac{0+2}{4}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = [tex]\frac{1}{2}[/tex] x - 2

Ngoc should predict that the home is located in Smavile based on the real estate advertisement

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

Function 1: p = 150 + 0.041a (Smavile)

Function 2: p = 250 + 0.198a (Fancyville )

Where

a = area

p = price

From the question, we have

a = area = 2800

p = price = 280000

Using the above as a guide, we have the following:

So, we have

Function 1: p = 150 + 0.041 * 2800 (Smavile)

Evaluate the expression

p = 264.8 -- false

Function 2: p = 250 + 0.198 * 2800 (Fancyville )

Evaluate the expression

p = 804.4 --- false

264.8  is closer to 280 than 804.4

Hence, the home is in Smavile

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The dimensions of the rectangle are length is 108 inches and width is 60 inches.

The area of Rectangle is length times of width.

The perimeter of a rectangle is 96 inches.

The length of the rectangle is 12 less than twice the width.

Length L=2W-12

Width=W

Perimeter=2(Length+Width)

=2(2W-12+W)

96=2(W-12)

Divide both sides by 2

48=W-12

Add 12 on both sides

60=W

Now length=2(60)-12

=120-12=108

Hence, the dimensions of the rectangle are length is 108 inches and width is 60 inches.

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Answer: C. 20

Step-by-step explanation:

Ley y be the duck mass, and x be the number of weeks

Our equation will be

y = 0.042x + 0.05

Then we plug 0.89 in the y

0.89 = 0.042x + 0.05

0.84 = 0.042x

x = 20 Weeks

So the answer is C. 20 weeks

The remainder is 5. To calculate this, first, divide 599 by 9 to get the largest multiple of 9 before 599. 5/9 < 1, so carry the 5 to the tens, 59/9 = 6 r 5, so carry the 5 to the digits. 59/9 = 6 r 5 again, so the largest multiple is 66. Multiply 66 by 9 to get 594, and subtract this from 599 to get 5, the remainder.

Answer:

22

Step-by-step explanation:

a) The co-efficient of x⁴y³ = -241920

b) The coefficient of x²y⁷ =  900

What Does an Expression Coefficient Mean?

The expansion is given by the following formula:

(a + b)ⁿ = Σⁿₓ=₀(ⁿₓ) aⁿ⁻ˣ bˣ, where

(ⁿₓ) = n! / (n-x)! k! and n! = 1.2..3.....n.

a) (-3x+4y)⁷ = ⁷C₀ (-3x)⁷(4y)⁰ + ⁷C₁ (-3x)⁶(4y)¹ + ⁷C₂ (-3x)⁵(4y)¹ + ⁷C₃ (-3x)⁴(4y)³ + ⁷C₄ (-3x)³(4y)⁴ + ⁷C₅ (-3x)²(4y)⁵ + ⁷C₆ (-3x)¹(4y)⁶ + ⁷C₇ (-3x)⁰(4y)⁷

The co-efficient of x⁴y³ = 35x - 27x³ * 256y⁴

= -241920x³y⁴

Hence, the coefficient of x⁴y³ = -241920.

b) (5x - y)⁹ = ⁹C₀(5x)⁹(-y)⁰ + ⁹C₁(5x)⁸(-y)¹ + ⁹C₂(5x)⁷(-y)² + ⁹C₃(5x)⁶(-y)³ + ⁹C₄(5x)⁵(-y)⁴ + ⁹C₅(5x)⁴(-y)⁵ + ⁹C₆(5x)³(-y)⁶ + ⁹C₇(5x)²(-y)⁷ + ⁹C₈(5x)(-y)⁸ + ⁹C₉(5x)⁰(-y)⁹

The coefficient of x²y⁷ = 36 * 25x² * y⁷

= 900x²y⁷

Hence, the coefficient of x²y⁷ = 900.

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Therefore, [tex]x^{2}[/tex] + 3 x -5 = 0 ,[tex]x^{2}[/tex] - x =0 and 7 [tex]x^{2}[/tex] + 14 x = 0  are quadratic equation.

Equation: a claim that two expressions with variable- and/or number-filled expressions are equivalent. Mathematical development has been sparked by the desire to find solutions to equations, which are really just questions.

Here,

Given:

[tex]x^{2}[/tex] + 3 x -5 = 0

[tex]x^{2}[/tex] - x =0

3 x + 7 .5 x - 7 = 0

7 [tex]x^{2}[/tex] + 14 x = 0

[tex]x^{3}[/tex]- 3 x2 + 1 = 0

x - 5 = 9 x + 7

The [tex]x^{2}[/tex] is present in equation which are quadratic

thus,

[tex]x^{2}[/tex] + 3 x -5 = 0

[tex]x^{2}[/tex] - x =0

7 [tex]x^{2}[/tex] + 14 x = 0

these following above equations are quadratic equation .

Therefore, [tex]x^{2}[/tex] + 3 x -5 = 0 ,[tex]x^{2}[/tex] - x =0 and 7 [tex]x^{2}[/tex] + 14 x = 0  are quadratic equation.

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It will take 5 weeks for every member to play each of the other members of the club.

What are the arrangements?

A strategy or preparation for something, especially for it to occur in a certain way: Two days a week, she had the plan to work from home. The motel was filled, so we had to find another place to stay.

Here, we have

A chess club meets every week and has 6 members.

Each member of the club plays one opponent each week.

We have to find out how many weeks will it take for every member to play each of the other members of the club.

Total number of matches played = (6×5)/2 = 15

Games per week = 3

Every member is to play each of the other members of the club = 15÷3= 5.

Hence, it will take 5 weeks for every member to play each of the other members of the club.

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The remainder will be constant if the divisor of a polynomial is a factor.

Given,

Polynomial division;

Divide the first term of the dividend by the first term of the divisor to divide polynomials using long division. The quotient's initial term is this. Dividend is calculated by multiplying the new term by the divisor. The new dividend is this difference.

We have to find the remainder if the divisor of a polynomial is a factor;

Here,

You know, from long division of regular numbers, that your residue (if there is one) has to be smaller than whatever you divided by. Since we're dividing by a linear factor (i.e., a factor whose degree on x is just an understandable "1"), the remainder in polynomial terms must be a constant value.

That is,

If a polynomial's divisor is a factor, the residual will always be a fixed number.

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