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The height of the telescope of 1 meter and width of 20 meters gives a distance of the focus from the vertex of 25 meters.

Given that the vertex is at the origin, we have;

(h, k) = (0, 0)

The equation of a parabola is presented as follows;

(x - h)² = 4•p•(y - k)

x² = 4•p•y

When x = 10, y = 1

Therefore;

p = 10² ÷ 4 = 25

The focus of the parabola = (h, k + p)

Which gives;

The focus of the parabola = (0, 0 + 25) = (0, 25)

The distance of the focus from the vertex is therefore;

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Answer:

8.15 miles

Step-by-step explanation:

Monday: 1 1/10 miles = 1.1

Multiply by 10 to get to 100

Wednesday: 4 4/5 miles = 4.8

Multiply by 20 to get to 100

Friday: 2 1/4 miles = 2.25

Multiply by 25 to get to 100

1.1 + 4.8 + 2.25 = 8.15 miles

Answer:

f(3)=-4; x=1

Step-by-step explanation:

Just use the graph

[tex]\huge\boxed{f(3)=-4}\\\huge\boxed{f(1\ \textsf{or}\ 4)=2}[/tex]

For this question, we just need to look at the graph.

[tex]f(3)=\ ?[/tex]

Go to [tex]3[/tex] on the x-axis and see what value from the y-axis it intersects with.

It's [tex]-4[/tex], right at the bottom of the little valley there.

[tex]f(?)=2[/tex]

For this part, we do the opposite. Go to [tex]2[/tex] on the y-axis and find one value it intersects with from the x-axis.

You can go with either [tex]1[/tex] or [tex]4[/tex] here.

Answer: B. 128

Step-by-step explanation:

According to the picture, the parallel side of the trapezoid are a= 10 cm and b = (10+4+8) cm= 22 cm respectively

The perpendicular distance between these parallel sides, h = 8 cm

We know,

 Area of trapezoid = {{(a+b)×h} ÷ 2

={(10+22)×8}÷2

=128

Answer:

48.2 metres

Step-by-step explanation:

Find the circumference of the circle, then ...

Explanation:

Circumference =2πr=2π(20)=40π meters

Arc Length =central∠360o×(Circumference)=138360×40π

=463π≈48.2 meters

hope that helps

The length of the arc of the circle is 48.2 meters.

The arc length formula for a circle is times the radius of a circle. Arc length ( [tex]\theta[/tex] x r) is a way to express the arc length formula in radians.

The length of the arc is calculated as:-

Circumference =2πr=2π(20)=40π meters

Arc Length  = Central ∠360° × (Circumference)

Arc Length  =138360×40π

Arc length =463π ≈ 48.2 meters

Therefore, the length of the arc of the circle is 48.2 meters.

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Answer:

3.

Step-by-step explanation:

The line segments are in the following ratio:-

2/10 = x/15

10x =  30

x = 3.

The game that is  used for the scenario above in terms of fair play is  using a balloon. Here, the player will hit the balloon.

The rule of play are:

This is a classic game with simple rules which are:

A scenario of the worksheet game whose expected value is 0 is given below:

Assume that it costs about $1 for a player to play the billon game and as such, if  the player hits a balloon, they will be given $3. what can you say. Can you say that it this game is fair or not? and who has the biggest advantage.

Solution

Note that a  game is ”fair” if the expected value is said to be 0. When a player is said to hits a balloon, their net profit often increase by $4.  So when the player do not hit a balloon, it drops to $1.

(4)(0.313) + (-1)(0.313)

= 0.939 approximately

Thus, the expected value is $0.939 which tells that the game is fair.

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Answer:

A is the correct answer...................................

The time William would arrive in town B IS 1 : 47 pm.

The first step is to determine the distance and the time of Dennis's travel.

Time = 14 hours (2 pm + 12) - 10 hours = 4 hours

Distance = time x average speed

4 x 52 = 208 miles

The second step is to determine the time of William's travel:

Distance / average speed = time

208 / 40 = 5.20 = 5 hours 12 minutes

Time William left for the trip = 10 am - 1 hour 25 minutes = 8 :35am

Time he would reach town B = 8 : 35am + 5 hours 12 minutes = 13 hours 47 minutes = 1 : 47 pm

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The number of pennies there are, given the types of coins you have are 5 pennies.

Since we have 5 dimes, we can set up the equation:

1/4 = 5/x

where x is the total number of coins.

Solving for x, we can cross-multiply:

1x = 45

x = 20

So we have a total of 20 coins.

Subtracting the number of quarters (3), dimes (5), and nickels (7), we get:

20 - 3 - 5 - 7 = 5 pennies

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Step-by-step explanation:

the first one

10 - 4x - 5 + 2x

-4x + 2x = -2x

10 - 5 = 5

so, in sum,

-2x + 5

Answer:

Step-by-step explanation: C. 28%

[tex]A = Pe^{rt}[/tex]

[tex]1649 = 100 \cdot e^{10r}\\16.49 = e^{10r}\\\ln{16.49} = 10r\\r = \frac{\ln{16.49}}{10} = 0.28\\[/tex]

Considering the slope of the lines, their relationship is given as follows:

They are not parallel because their slopes are not equal.

The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:

In this problem, their slopes are given as follows:

Different slopes, multiplication different of -1, hence the correct option is given by:

They are not parallel because their slopes are not equal.

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Answer:

C. They are not parallel because their slopes are not equal.

In order to prove that a line that is parallel to one side of a triangle divides the other sides proportionally, you can use the Cross Product Property.

If a line is parallel to one side of a triangle and divides the other two sides, those sides would be proportional to each other according to the Triangle Proportionality Theorem.

This can be shown as:

AB² = BC x BD

Where the two sides can be multiplied to get the length of the side the parallel line crossed from.

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Answer:

5√3/3

Step-by-step explanation:

To get the shorter leg of the triangle, we have to divide the longer leg by √3: 5/√3

To solve, multiply by √3/√3: 5/√3 * √3/√3 = 5√3/√9 = 5√3/3

Answer:

The shadow cast by the tree is 80 meters long.

Step-by-step explanation:

Flagpole:

object/shadow

25/50 = 1/2

Tree:

object/shadow

40/x

Solve for x:

1/2 = 40/x

x = 80

Answer:

It would be C

Step-by-step explanation:

The fraction equal to 4/5 is 8/10 so closest to 8/10 is 8/11

1st transformation: A vertical translation of the figure down by 8 units

2nd transformation: Shows a reflection on both axis and vertical translation up the plane by 8 units

Transformation is a way of changing the position of an object on an xy-plane.

For the translation

(x, y)-> (x, y-8)

It shows a vertical translation of the figure down by 8 units while the translation;

(x, y - 8) -> (-x, -y)

shows a reflection on both axis and vertical translation up the plane by 8 units

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Answer:

x = 8

Step-by-step explanation:

An Equilateral triangle is a triangle in which all three sides and angles are equal. The value of each angle of an equilateral triangle is 60 degrees therefore we get the equation 9x - 12 = 60

Add 12 from both sides to isolate the 9x leaving us with:

9x = 72

Divide both sides by 9 to give us x, which is

x = 8

Answer:

300°

Step-by-step explanation:

Given from the diagram:

Angle a° = 180° (Single angle on a straight line)

Angle c° + 60° = 180° (Sum of angles on a straight line)

Angle c° = 180° - 60° = 120°

Angle a° + c° = 180° + 120° = 300°

Answer:

a + c = 300°

Step-by-step explanation:

a = 180°

c = 180° -  60° = 120°

a + c = 180° + 120° = 300°

Answer:

D

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex] , then

[tex]log_{2}[/tex] x = 4.3 ⇒ x = [tex]2^{4.3}[/tex] ≈ 19.70 ( to 2 dec. places )

The inequality that can be used to represent the situation is 7.50 + 14x ≤ 60 where x ≤ 3.75

7.50 + 14x ≤ 60

14x ≤ 60 - 7.50

14x ≤ 52.50

x ≤ 52.50 / 14

x ≤ 3.75

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p = 6.98

The mean number of words per minute (WPM) read by sixth graders is 86 with a variance of 225. If 44 sixth graders are randomly selected then,

The z-score of the information given is:

z=(x-μ)/σ

where

μ-mean

σ- standard deviation

from the information given:

x=3.71

μ=86

σ=√225 = 15

hence, the probability that the sample mean would differ from the population mean by less than 3.71 WPM is

z = (3.71 + 86)/15

z = 5.98

thus,

p = 1 + 5.98 = 6.98

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Answer:

B. 35

Step-by-step explanation:

[tex] {12}^{2} + {x}^{2} = {(x + 2)}^{2} [/tex]

[tex]144 + {x}^{2} = {x}^{2} + 4x + 4[/tex]

[tex]144 = 4x + 4[/tex]

[tex]4x = 140[/tex]

[tex]x = 35[/tex]

Answer:

B.35 is the correct answer

Step-by-step explanation:

. Hello!

As, we know Pythagorean theorem is

a²+b²=c²,

where a&b are two sides of the triangle and c is it's hypotenus.

so, assuming 12=a, x=b and x+2i=c

If you have any questions ask me thx

The probability that the sample proportion will be less than 0.04 is 0.8995 or 89.95%.

The true proportion (p) is given to be 0.03.

Therefore, Mean (μ) = p = 0.03.

The standard error of sampling distribution can be calculated using the formula σ = √[{p(1 - p)}/n], where n, is the sample size, that is, n = 476.

Therefore, σ = √[{0.03(1 - 0. 03)}/476] = 0.00782.

Since, np = 14.28 and n(1 - p) = 461.72 are both greater than 5, we assume the sample is normally distributed.

Since, we are asked to find the probability that the sample proportion is less than 0.04, we using our calculator, enter as following:

Normalcdf(-100000000,0.04,0.03,0.00782), which gives us the value 0.8995 or 89.95%.

Thus, the probability that the sample proportion will be less than 0.04 is 0.8995 or 89.95%.

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The shape of the cross section is a square. The correct option is the D. SQUARE

From the question, we are to determine shape of the cross-section formed.

A cross-section is seen when a three-dimensional image is cut by a plane.

The given figure is a square pyramid.

In the given diagram, plane S is a square. The intersection of plane S with the square pyramid gives square cross-section as shown in the figure.

Thus, the shape of the cross section is a square.

A shows a parallelogram

B shows a triangle

C shows a trapezoid

D shows a square

Hence, the shape of the cross section is a square. The correct option is the D. SQUARE

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