Out of a population of 1,500 students, 100 were asked by a random sampling to choose their favorite national park. their responses are shown in the table below. national parks favorite park number of students acadia 19 carlsbad caverns 14 rocky mountain 30 grand canyon 23 yosemite 14 using proportional reasoning, about how many students out of the 1,500 would you expect to pick yosemite for their favorite national park? 14 86 210 244

Answer:

18.8%

Step-by-step explanation:

For calculating this, focus on one part of the table :

There are 32 students who do not like sandwiches, and 6 of them do not like pies. Take this a proportion :

Students who don't like sandwiches also don't like pie is the 2 nd box on 2 nd line

Probability

Option D

Answer:

It's the the 4th one. 6.3.3

Answer:

a²+1/a² = 7

Step-by-step explanation:

Given, a = (3+√5)/2

We have to find the value of a² + 1/a².

1/a = 1/((3+√5)/2) = 2/(3+√5)

By taking conjugate,

2/(3+√5) = 2/(3+√5) × (3-√5)/(3-√5)

= 2(3-√5) / (3+√5)(3-√5)

By using algebraic identity,

(a - b)(a + b) = a² - b²

(3+√5)(3-√5) = (3)² - (√5)²

= 9 - 5

= 4

2(3-√5) / (3+√5)(3-√5) = 2(3-√5) / 4

So, 1/a = (3-√5)/2

Now, a² = [(3+√5)/2]²

= (3+√5)²/4

By using algebraic identity,

(a + b)² = a² + 2ab + b²

(3+√5)² = (3)² + 2(3)(√5) + (√5)²

= 9 + 6√5 + 5

= 14 + 6√5

a² = (14+6√5)/4

= 2(7+3√5)/4

a² = (7+3√5)/2

Now, 1/a² = [(3-√5)/2]²

= (3-√5)²/4

By using algebraic identity,

(a - b)² = a² - 2ab + b²

(3-√5)² = (3)² - 2(3)(√5) + (√5)²

= 9 - 6√5 + 5

= 14 - 6√5

1/a² = (14-6√5)/4

1/a² = (7-3√5)/2

a²+1/a² = (7+3√5)/2 + (7-3√5)/2

= 7/2 + 3√5/2 + 7/2 - 3√5/2

= 7/2 + 7/2

= 7

Therefore, a²+1/a² = 7

the answer is b

Step-by-step explanation:

hope this helps if not let me know have a blessed day

Answer:

See below for answers and explanation

Step-by-step explanation:

A statistical question has variability in collecting the data, and doesn't have one definitive answer:

Question 1: How many of Mrs. Malone's students earned an A for the first nine weeks? This is not a statistical question because you can narrow down exactly how many.

Question 2: How many students missed question #5 on Mrs. Malone's math test yesterday? This is not a statistical question because you can easily take all the worksheets done on the math test and find an exact number.

Question 3: How many of Mrs Malone's students turn in their homework each day? This is a statistical question because not every student will consistently turn in their homework each day, so there will be variability while collecting that data.

Hence, Question 3 is a statistical question

Answer:

A = 81π units²

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius ) , then

A = π × 9² = 81π units²

Answer:

R' (- 1, 6 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

R (- 1, - 6 ) → R' (- 1, 6 )

Answer:

the answer should be (-1, -6) because remember when you are doing these kind of problems of pluging in the points in a coordinate plane remember the quadraunts  to help you know everything you need in case of future problems.

So back remember first is x and then y so when we analyze the point the x is -1 and the y is -6 so the point r represnts= (-1,-6)

so hopefully that is the correct answer and have a great day.

remember first is x and then y

Step-by-step explanation:

Answer:

The first graph.

Answer:

A

Step-by-step explanation:

Answer:

0.25π

Step-by-step explanation:

→ Expand the bracket

4 × cos²Ф = 2

→ Divide both sides by 2

cos²Ф = 0.5

→ Square root both sides

cos Ф =  [tex]\frac{\sqrt{2} }{2}[/tex]

→ Inverse cosine  [tex]\frac{\sqrt{2} }{2}[/tex]

cos⁻¹ (   [tex]\frac{\sqrt{2} }{2}[/tex]  ) = 0.25π

Answer:

Answer:

0.25π

Step-by-step explanation:

→ Expand the bracket

4 × cos²Ф = 2

→ Divide both sides by 2

cos²Ф = 0.5

→ Square root both sides

cos Ф =  

→ Inverse cosine  

cos⁻¹ (     ) = 0.25π

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 10,000,000 because u have to do 10x10x10x10x10x10x10

So basically I did the most easiest way possible with is multiply 1 and 1 and then add the zero and I got 10 so if u add the zeros up 6 more times then we get 10 million or 10,000,000.

The value of cos x⁰ from the information given is; g/h.

According to the task content;

The value of cos x° from the information contained in the task content is required.

From conventional Trigonometry;

It follows that tan x = sin x/cos x.

On this note, it follows that;

cos x⁰ = sin x⁰/tan x⁰.

cos x⁰ = 6/h ÷ 6/g

cos x⁰ = g/h

Ultimately, the value of Cos x⁰ by evaluation is g/h.

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Answer:

cos x° = g divided by h

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

the ratio of b : c is the cos77° , that is

cos77° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{b}{c}[/tex] ≈ 0.224951054.

Answer:

17

Step-by-step explanation:

f(x) = 2x+7

Let x =5

f(5) = 2*5 +7

     = 10+7

    = 17

Answer: 97/125

Step-by-step explanation:

The measure of angle DAB in the circle shown with the given arc length is: 2.23 radians.

Arc length = θ × r, where r is the radius of the circle, and θ is the central angle in radians.

Given the following:

Length of arc = 6.47 cm

Radius (r) = 2.9 cm

θ = m∠DAB

Plug in the values into the arc length formula:

6.47 = θ × 2.9

6.47/2.9 = θ

θ = 2.23 radians

m∠DAB = 2.23 radians

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Answer:

DAB = 2.23 radians

Hope this helps!

Step-by-step explanation:

The area of the rectangle in the form of a polynomial is 40(x² + 6x + 5). If the width is 160 ft, then the area of the rectangle is 57,600 square ft.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.

If the length and width of the rectangle are (10x + 10) and (4x + 20). Then the area of the rectangle will be

Area = (10x + 10)(4x + 20)

Area = 40x² + 200x + 40x + 200

Area = 40x² + 240x + 200

Area = 40(x² + 6x + 5)

If the width is 160 feet then the value of x will be

4x + 20 = 160

       4x = 140

         x = 35

Then the area of the rectangle will be

Area = 40(35² + 6 × 35 + 5)

Area = 40(1225 + 210 + 5)

Area = 40 (1440)

Area = 57,600 square ft

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Answer:

Step-by-step explanation:

Givens

4 scones

1 loaf of bread

Total cost = 3.30

Equation

Let the loaf of bread = b

Let the scones = s

Cost = b + 4s

Solution

Substitute the givens into the equation

b + 4s = Cost

90 + 4s = 3.30                  Subtract 90 from both sides

90-90 + 4s = 3.30-90      Combine

4s = 2.40                          Divide by 4

4s/4 = 2.40/4                

s = 0.6 of a pound

Answer: 1 scone = 60 pence.

Answer:

v = 37 yards

Step-by-step explanation:

Volume of a rectangular prism = width × length × height

Given:

Substituting the given values into the formula and solving for v:

⇒ 51615 = v × 93 × 15

⇒ 51615 = 1395 v

⇒ v = 51615 ÷ 1395

⇒ v = 37

Answer:

v = 37 yds

Step-by-step explanation:

Volume of a rectangular prism: length × width × height

V = L×W×H

Substitute the values above and solve for v:

51,615 = 93 × v × 15

51,615 = 1395v

51,615/1395 = 1395v/1395

37 = v

Final answer: 37 yds

Hope this helps!

Using a system of equations, it is found that the cost of a paint set is of $19.50.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

Cara brought $34.50 to the art supply store, bought one of each item, and had $2.00 left, hence:

x + y + z = 32.50.

The sketchbook cost half the cost of the paint set, hence:

y = 0.5x.

The brush cost one third of the sketchbook, hence:

z = 0.3333(0.5x) = 0.1667x.

Then, to solve for x:

x + y + z = 32.50

x + 0.5x + 0.1667x = 32.50

x = 32.50/1.6667

x = 19.50.

The cost of a paint set is of $19.50.

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The total percentage by which Jan's groceries were discounted is 16.65% approximately. (Option C). See the attached and the explanation below.

Step 1 - Reverse engineer, the figures to get the original prices first.

Step 2 - Sum up all the discounted prices as well as the Original prices then find the difference.

Step 3 - Divide the difference by the original price to get the percentage difference

$3.75/$22.47 = 16.68% (Nearest answer is Option C)

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Answer:

See below ~

Step-by-step explanation:

Question 12

Question 17

Part A

Part B

The equation that represents the directrix of y² = 12x is x = -3

The parabola is given as:

y² = 12x

The general equation of a parabola is

(y-y₀)² = 4a(x-x₀)

Where the equation of the directrix is x = x₀ - a

By comparing (y-y₀)² = 4a(x-x₀) and y² = 12x, we have:

4a = 12 and x-x₀ = x

Solve for a in 4a = 12

a = 3

Solve for x₀ in x-x₀ = x

x₀ = 0

Substitute a = 3 and x₀ = 0 in x = x₀ - a

x = 0 - 3

Evaluate

x = -3

Hence, the equation that represents the directrix is x = -3

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Based on the calculations, the two lines have the same slope but different intercepts and as such are parallel.

In Geometry, two lines are considered to be parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

For two perpendicular lines, we have:

m₁m₂ = -1.

From line k, we have this equation:

y = 1/3x - 2

From line m, we have this equation:

-2x + 6y = 18.

6y = 18 + 2x

y = 18/6 + 2/6x

y = 1/3x + 3.

Therefore, we can deduce that the two lines have the same slope (1/3) but different intercepts and as such are parallel.

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Answer:

fraction :4

Step-by-step explanation:

Answer:

C, ∠DEO ≅ ∠FEO

Step-by-step explanation:

The bisector EO bisects the angle ∠DEF, an interior angle of ΔDEF.

This means the angle is divided into 2 equal angles.

⇒ ∠DEO ≅ ∠FEO

Answer:

Left side                                  Right side

1                                                   3

2                                                  2

3                                                  1

Step-by-step explanation:

left side on the picture right side on the picture

The length of BC= 7√2 and BD = 7.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given:

AD= 7, AC= 14

In Δ BDC

cos 45 = B/ H

1/√2 = 7/ BC

BC= 7√2

In Δ BDC

sin 45 = P/H

1/√2= BD / 7√2

BD = 7

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Answer:

The first graph

Step-by-step explanation:

-2x is the key here, when you add a subtraction sign to the x-axis it goes right.

+2x would be the graph on the bottom because it is translated to the left.

So the first graph on your picture is the answer.

Answer+Step-by-step explanation:

x² – 2x + 3 = (x - 1)² + 2

Then

The vertex of the parabola is the point (1 , 2)

then

The graph number 1 (on top) is the one which represents f

Answer:

60^2/5

Step-by-step explanation:

2^2/5 × 5^2/5

=(12×5)^2/5

=60^2/5

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

[tex]\huge\textsf{12}}^ \mathsf{^ {\dfrac{2}{5}}}\ \huge\boxed{\times}\ \huge\textsf{5}^\mathsf{^ \dfrac{2}{5}}[/tex]

[tex]\huge\boxed{=}\huge\textsf{ 2.70192 }\huge\boxed{\times}\huge\textsf{ 1.903654}[/tex]

[tex]\huge\boxed{= }\huge\textsf{ 60}^\mathsf{\dfrac{2}{5}}[/tex]

[tex]\huge\boxed{\approx}\huge\textsf{ 5.143521}[/tex]

[tex]\huge\text{Therefore, the answer is: \boxed{\textsf{60}^\mathsf{^\dfrac{2}{5}}}}\huge\checkmark[/tex]

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

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