A survey reported that 4 out of every 10 students at Pinewood Middle like chocolate ice cream. Which two ratios correctly represent this comparison?​

Answer: y = 4x + 5

Step-by-step explanation:

Rearranging 4x-y = 1 we get y = 4x-1 as the equation of the line.

Since the new line is parallel to y=4x-1, that means the slopes are equal. Therefore, the slope of the line is 4.

So, the equation of the line is y = 4x+b

To figure out b, we can plug in the point (-2,-3) into the equation.

So -3 = -2*4 + b

-3 = -8 + b

And we get b = 5.

Therefore, the equation of the line is y = 4x + 5

Answer:

y = 4x + 5

Step-by-step explanation:

First, we need to find the slope of the given equation: 4x - y = 1

Subtract 4x from both sides

4x - y = 1

- 4x      - 4x

-y = 1 - 4x

Divide both sides by -1 to make the y variable positive

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

y = -1 + 4x

This means the slope of this equation is 4

Our parallel equation will be y = 4x + b

Plug in the given coordinates

-3 = 4(-2) + b

-3 = -8 + b

Add 8 to both sides

-3 = -8 + b

+ 8   + 8

b = 5

Plug in the new b into the original parallel equation

y = 4x + 5

The tangents of the acute angles in the right triangle gives:

tan(G) = 2

tan(H) = 1/2

It should be noted that tangent is the ratio of opposite over adjacent. Thus:

tan(angle) = opposite/adjacent

So for reference angle G, we say,

tan(G) = JH/GJ = 2/1 = 2

We'll treat tan(H) in a similar fashion, but the opposite and adjacent sides swap roles. That means we'll apply the reciprocal to the result above to get 1/2 for tan(H)

So we have this interesting property where

tan(G)*tan(H) = 2*(1/2) = 1

In general,

tan(A)*tan(B) = 1 if and only if A + B = 90 degrees

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The perimeter of scale drawing of Central Park is 30 centimeter.

The area of scale drawing of Central Park is 31.25 square centimeters.

What is perimeter?

The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.

Given that Central Park is a rectangular park in New York City

The measured length is 12.5 centimeters

The measured width is 2.5 centimeters

The perimeter of scale drawing of Central Park is given as:

Given is a rectangular park

perimeter of rectangular = 2(length + width)

perimeter of rectangular = 2(12.5 + 2.5)

perimeter of rectangular = 2(15) = 30

Thus perimeter is 30 centimeter

The area of scale drawing of Central Park is given as:

area = length x width

area = 12.5 x 2.5 = 31.25 cm²

Thus area of rectangular park is 31.25 square centimeters

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The value of the missing side lengths x and y are 5√2 and 5 respectively.

The figure in the image is a right triangle.

Angle θ = 45 degree

Hypotenuse = x

Opposite to angle θ = y

Adjacent to angle θ = 5

To solve for side x and side y, we use the trigonometric ratio.

Note that:

Cosine = adjacent / hypotenuse

tangent = opposite / adjacent

Solving for x:

Cosine = adjacent / hypotenuse

Plug in the values

cos( 45 ) = 5/x

x = 5 / cos( 45 )

x = 5√2

Solving for side y:

tangent = opposite / adjacent

Plug in the values

tan( 45 ) = y/5

y = tan( 45 ) × 5

y = 5

Therefore, the value of side length x is 5 units.

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Answer:

(x) ∠CAB

Step-by-step explanation:

In ΔCOD and ΔBOA

\(\frac{OA}{OB} = \frac{OD}{OC} \\\\\implies \frac{OC}{OB} = \frac{OD}{OA}\)

Also,

∠COD = ∠BOA (vertically opposite angles)

⇒ ΔCOD and ΔBOA are similar

⇒ ∠CDO = ∠BAO

⇒ ∠CDB = ∠BAC

⇒ ∠CDB = ∠CAB

Answer:

Original price = t = $24

Expression = t + 0.05t

—-

New price = t + 0.05t = 24 + (0.05*24) = $25.20

—-

Have a nice day!!

Answer:

$25.20

Step-by-step explanation:

Original price = t = $ 24

New price = 1.05*24

                 = 25.20

Just multiply 1.05 by 24

Answer:

Option 2) Sin 35 = \(\frac{5}{x}\)

Step-by-step explanation:

Sin 35 = \(\frac{opposite }{hypotenuse}\)

Where opposite = 5' and hypotenuse = x(unknown)

=> Sin 35 = \(\frac{5}{x}\)

Answer: 26.4347826087

Step-by-step explanation:

608 divided by 23 = 26.4347826087.

Answer:

8 suits

Step-by-step explanation:

Divide 30 m by 3 \(\frac{3}{4}\) m , or 30 ÷ 3.75 , then

30 ÷ 3.75 = 8

Then 8 suits can be made from 30 m of cloth

Answer: 7x + 1

Step-by-step explanation:

(6x-4)+(x+5)

Step 1: Remove Parentheses:

              6x-4+x+5

Step 2: Combine Like Terms:

             7x +1

A number of nurses at Sotik Health Centre raised Sh 144,000 for land.

The nurses at Sotik Health Centre successfully raised Sh 144,000 to acquire land. Their collective effort and determination allowed them to reach their fundraising goal.

The raised funds will be utilized to purchase land, which indicates their commitment to expanding the health center's facilities or developing new infrastructure to better serve their patients.

This achievement highlights the dedication and unity among the nurses, as they recognized the importance of investing in the future of their workplace.

The nurses' initiative and collaborative spirit demonstrate their commitment to improving healthcare services and ensuring a more sustainable and efficient environment for both the staff and patients at Sotik Health Centre.

The decision of the nurses at Sotik Health Centre to raise Sh 144,000 for land exemplifies their proactive approach to addressing the center's needs. Acquiring land is a crucial step in expanding the facilities or establishing new infrastructure.

With the funds raised, the nurses have the opportunity to enhance the capacity of the health center and provide a wider range of services to the community. This achievement also reflects the nurses' strong sense of ownership and responsibility towards their workplace.

By actively participating in fundraising efforts, they not only contribute financially but also foster a sense of unity and collaboration within the team. Their dedication and commitment to improving healthcare demonstrate their unwavering commitment to their profession and the well-being of the patients they serve.

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Answer:

1/ 16

Step-by-step explanation:

Flipping a coin = HT ( 2 possibilities)

Hence, total possibility (n) of flipping 4 coins

n = 2^4 = 2 * 2 * 2 * 2 = 16 possible outcomes

(HHHH, THHH, HHHT, THHT, HHTH, THTH, HHTT, THTT, HTHH, TTHH, HTHT, TTHT, HTTH TTTH, HTTT, TTTT

Probability (A) = required outcomes of A / total possible outcomes

Hence, probability that all coins comes up head :

Number of required outcome = 1

Total possible outcomes = 16

Hence,

P(all heads) = 1/16

Using the binomial distribution, it is found that there is a 0.0625 = 6.25% probability that all four coins will come up heads.

For each coin, there are only two possible outcomes, either it is heads, or tails. The outcome of each coin is independent of other coins, hence, the binomial distribution is used to solve this question.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The probability that all four coins will come up heads is P(X = 4), hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 4) = C_{4,4}.(0.5)^{4}.(0.5)^{0} = 0.0625\)

0.0625 = 6.25% probability that all four coins will come up heads.

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Answer:

negative

Step-by-step explanation:

we know this because a negative divided by a positive is a negative

Answer:

Step-by-step explanation:

= -125 ÷ 5

= -25

It's negative

Answer:

3

Step-by-step explanation:

The solution to the system of equations is the point of intersection of the graphs of the equations.

The solution is point (3, 2).

An ordered pair is of the form (x, y). The x-coordinate of point (3, 2) is 3.

Answer: 3

Answer:

You can try searching it up or going to math.way

Step-by-step explanation:

Answer:

x=1.25 and y=-5.5

Step-by-step explanation:

2x+y=-8, 2x=-y-8 or 4x=-2y-16. Plug this value in the second equation, we have - 2y-16-2y=6, y=-5.5. Plugging this in any equation we have, x=1.25

Answer:

Step-by-step explanation:

If x - 1 is a factor of the cubic, then 1 should result in 0 when you put it in the cubic for x. Does it?

f(1) = 2(1)^3 - 15(1)^2 + 22(1) + 15

f(1) = 2 - 15 + 22 + 15

f(1)= 24.

No the result is not zero. So x - 1 is not a factor.

However there must be something that makes this cubic go to zero. The easiest way to find it is to graph it.

The numbers that do make this zero are -0.5, 3, 5

Which mean that the factors are (2x+1)(x-3)(x - 5)

Option (b) is the correct answer: Perpendicular segments.

Perpendicular rays, perpendicular segments, perpendicular lines, and parallel lines are important concepts in geometry that describe the relationship between lines and line segments.

1. Perpendicular Rays: Perpendicular rays are two rays that intersect at point and form a right angle (90 degrees) at the point of intersection. The rays extend indefinitely in opposite directions from the point of intersection.

2. Perpendicular Segments: Perpendicular segments are line segments that intersect at a right angle. They share a common endpoint but do not extend indefinitely like rays. The right angle is formed at the point of intersection.

3. Perpendicular Lines: Perpendicular lines are lines that intersect at a right angle. They continue indefinitely in opposite directions and form four right angles at the point of intersection. Perpendicular lines are often denoted by a symbol ⊥.

4. Parallel Lines: Parallel lines are lines that never intersect. They remain equidistant from each other at all points. Parallel lines have the same slope and do not converge or diverge. In Euclidean geometry, parallel lines are denoted by a double vertical line symbol (||).

Understanding these concepts is fundamental in geometry as they help define angles, shapes, and spatial relationships. The properties of perpendicular and parallel lines play a crucial role in various geometric theorems and applications.

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Answer:

MAD would be more similar than mean

Step-by-step explanation:

Without doing any calculations, I assumed that the average value for each neighbor is different since their dot plots surround different areas. The MAD is the mean absolute deviation where it shows how distributed are the dot plots compared to the average value. In this case, I can tell that both neighborhoods having a very similar distribution of dot plots relative to their average/mean. Hope this helps!

The blue figure is moved 5 units to the right (T(5, 0)), reflected in the y-axis (r(y-axis)), and then rotated 90 degrees counterclockwise (R(-90)).

Translation: Move the blue figure 5 units to the right (translation of 5 units to the right, denoted as T(5, 0))

Reflection: Reflect the figure in the y-axis (denoted as r(y-axis))

Rotation: Rotate the figure 90 degrees counterclockwise (denoted as R(-90))

The series of transformations that moves the blue figure to the red figure is T(5, 0) followed by r(y-axis) followed by R(-90).To better understand this, let's break down the transformations. The first transformation is a translation, which is a movement of a figure from one location to another. In this case, the figure is being moved 5 units to the right. This is denoted as T(5, 0).The second transformation is a reflection, which is a flip of a figure over a line or axis. In this case, the figure is being reflected in the y-axis. This is denoted as r(y-axis).The third transformation is a rotation, which is a turn of a figure around a point. In this case, the figure is being rotated 90 degrees counterclockwise. This is denoted as R(-90).Therefore, the series of transformations that moves the blue figure to the red figure is T(5, 0) followed by r(y-axis) followed by R(-90).

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The volume of the shape is 490cm³

A prism is a solid shape that is bound on all its sides by plane faces. prism is named after the shape of these bases.

The base of this prism is rectangular. The volume of a prism is expressed as;

V = base area × height

base area = 7 × 10 = 70cm²

height = 7cm

the volume of the shape = 70× 7 = 490cm²

therefore the volume of the shape is 490cm³.

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a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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Answer:

1. 5000

2. 500

3. 50

4. 50

5. 50

6. 0.5

Answer: 42

Step by step:

42 is divisible by both 7 and 2

Answer:

44

Step-by-step explanation:

4 x 11 = 44

2 x 22 = 44

Answer:

C = 10π

Step-by-step explanation:

C = Dπ

D = 10

C = 10π

Answer:

see below

Step-by-step explanation:

The circumference of a circle is given by

C = pi *d

C = 10 pi m

We can approximate pi by 3.14

C = 3.14 * 10

C =31.4m

or we can approximate pi by using the pi button

C =31.41592654m

Answer:

Step-by-step explanation:

let number be X

so,

X + 40 = 450

X = 450 - 40

X = 410

FOLLOW ME

Hi there!

It would be 410!

1.Subtract 450 by 40 / subtract both terms:

\(450-40=410\)

Check:

\(410+40=450=450-40=410\)

Answer:

Y=51.34019175

Step-by-step explanation:

We first use Pythagoras theorem to find the hypo...

\( \sqrt{ {8 }^{2} + {10}^{2} } = 12.8062487\)

After we use sine rule

12.8062487/sin90 = 10/siny

Sin y=10sin90/12.8062487

Y=51.34019175

Answer:

6 and 8

Step-by-step explanation:

have a great day luv