Work out the length of AG in the cuboid below.

The ratiο οf the amοunt spent οn staff salaries tο the tοtal budget fοr the yοuth prοgrams is 1:5.

A ratiο is an οrdered pair οf numbers a and b, written a / b where b dοes nοt equal 0. A prοpοrtiοn is an equatiοn in which twο ratiοs are set equal tο each οther. Fοr example, if there is 1 bοy and 3 girls yοu cοuld write the ratiο as 1 : 3 (fοr every οne bοy there are 3 girls).

If 80 cents οf every dοllar gοes directly tο prοgram services, then 20 cents οf every dοllar is spent οn staff salaries.

This can be written as a ratiο οf 20 cents tο 100 cents, οr simplified tο 1:5.

Therefοre, the ratiο οf the amοunt spent οn staff salaries tο the tοtal budget fοr the yοuth prοgrams is 1:5.

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Answer:

Answer would be triangle CAB

Answer:

=2

Step-by-step explanation:

You divide by five on each side of the = and then after that you should have X equals two!

[tex]$$16[(x_2 - x_1)^2 + (y_2 - y_1)^2]x^2 - 32(x_2 - x_1)x^3 + 16(x_2 - x_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]x + 16[(y_2 - y_1)^2 + (x_2 - x_1)^2]y^2 - 32(y_2 - y_1)y^3 + 16(y_2 - y_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]y + [(x_2 - x_1)^2 + (y_2 - y_1)^2 - 180^2]^2 = 0$$[/tex]

this is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola.

What is hyperbola ?

A hyperbola is a type of conic section that has two separate parts, called branches, which are mirror images of each other. It is defined as the set of all points in a plane, such that the difference between the distances from two fixed points, called foci, is a constant. Hyperbolas have many applications in science, engineering, and mathematics.

Given two LORAN transmitters located at the coordinates [tex]$(x_1, y_1)$[/tex] and [tex](x_2, y_2)$[/tex], where unit distance on the coordinate plane is measured in miles.

Let the coordinates of the receiver be [tex](x,y)$.[/tex]

The distance from the receiver to the first transmitter is given by [tex]$\sqrt{(x - x_1)^2 + (y - y_1)^2}$[/tex], and the distance from the receiver to the second transmitter is given by [tex]\sqrt{(x - x_2)^2 + (y - y_2)^2}$.[/tex]

Since the difference in the distances from the receiver to these transmitters is 180 miles, we have:

[tex]$$\sqrt{(x - x_1)^2 + (y - y_1)^2} - \sqrt{(x - x_2)^2 + (y - y_2)^2} = 180$$[/tex]

Squaring both sides, we get:

[tex]$$(x - x_1)^2 + (y - y_1)^2 - 2\sqrt{(x - x_1)^2 + (y - y_1)^2} \sqrt{(x - x_2)^2 + (y - y_2)^2} + (x - x_2)^2 + (y - y_2)^2 = 180^2$$[/tex]

Rearranging, we get:

[tex]$$(x - x_1)^2 + (y - y_1)^2 - (x - x_2)^2 - (y - y_2)^2 = 4\sqrt{(x - x_1)^2 + (y - y_1)^2} \sqrt{(x - x_2)^2 + (y - y_2)^2} - 180^2$$[/tex]

Using the identity $a^2 - b^2 = (a + b)(a - b)$, we can simplify the left-hand side as:

[tex]$$4x(x_2 - x_1) + 4y(y_2 - y_1) = 4\sqrt{(x - x_1)^2 + (y - y_1)^2} \sqrt{(x - x_2)^2 + (y - y_2)^2} - 180^2$$[/tex]

Squaring both sides again and simplifying, we get:

[tex]$$16[(x_2 - x_1)^2 + (y_2 - y_1)^2]x^2 - 32(x_2 - x_1)x^3 + 16(x_2 - x_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]x + 16[(y_2 - y_1)^2 + (x_2 - x_1)^2]y^2 - 32(y_2 - y_1)y^3 + 16(y_2 - y_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]y + [(x_2 - x_1)^2 + (y_2 - y_1)^2 - 180^2]^2 = 0$$[/tex]

this is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola.

Therefore, [tex]$$16[(x_2 - x_1)^2 + (y_2 - y_1)^2]x^2 - 32(x_2 - x_1)x^3 + 16(x_2 - x_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]x + 16[(y_2 - y_1)^2 + (x_2 - x_1)^2]y^2 - 32(y_2 - y_1)y^3 + 16(y_2 - y_1)[(y_2 - y_1)^2 + (x_2 - x_1)^2 - 180^2]y + [(x_2 - x_1)^2 + (y_2 - y_1)^2 - 180^2]^2 = 0$$[/tex]

this is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola.

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The number of smaller card that could be cut from the larger rectangular card is 64.

Yuri has a large rectangular card measuring 1.2 meters by 0.8 meters, he wants to cut it up to make small rectangular cards each measuring 13 cm by 11.5 cm.

Let's convert the units.

1.2 m = 120 cm

0.8 = 80 cm

Therefore, let's find the area of the rectangular card.

area of the large rectangular card = lw

where

area of the large rectangular card = 120 × 80

area of the large rectangular card = 9600 cm²

area of each small rectangular card = 11.5 × 13.5

area of each small rectangular card = 149.5 cm²

Therefore,

largest number of card that can be cut out from the larger card = 9600 / 149.5 = 64.2140468227

largest number of card that can be cut out from the larger card ≈ 64

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On solving the provided question we cans ay that As a result, the ball function remains in the air for 5 seconds.

Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.

The function f(x) = -6t(t-5) reflects the football's height at time t. When the football lands, its height will be zero.

To determine the time the ball is in the air, we must first determine when f(t) = 0. As a result, we may set the equation to zero and solve for t:

-6t(t-5) = 0

This equation is valid for t = 0 or t = 5. When the ball is tossed, time t = 0 occurs, and time t = 5 occurs when the ball strikes the ground. The time the ball is in the air is calculated as follows: time in air = t final - t initial = 5 - 0 = 5 seconds.

As a result, the ball remains in the air for 5 seconds.

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Answer: 13/25

Step-by-step explanation:

Answer:

$18 were given to each class

Step-by-step explanation:

90÷5=18

Answer:

x = 13.44 (2 d.p.)

y = 13.44 (2 d.p.)

Step-by-step explanation:

The interior angles of a triangle sum to 180°. Therefore, the missing angle of the given triangle is 45°. This means the triangle is a 45-45-90 triangle.

A 45-45-90 triangle is a special right triangle in that the measures of its sides are in the proportion x : x : x√2 where:

As the given triangle is a 45-45-90 triangle, sides x and y are the same length.

As the hypotenuse (side opposite the right angle) is 19 units in length, then x√2 = 19.  To find the length of x (and y), solve for x:

[tex]\implies x\sqrt{2} = 19[/tex]

[tex]\implies \dfrac{x\sqrt{2}}{\sqrt{2}} = \dfrac{19}{\sqrt{2}}[/tex]

[tex]\implies x= \dfrac{19\sqrt{2}}{2}[/tex]

[tex]\implies x=13.44\; \sf units\;(2\;d.p.)[/tex]

Answer:

2x+15

Step-by-step explanation:

Answer:

2x + 15

Step-by-step explanation:

First, we are doubling x.

We know that doubling is the same thing as multiplying by 2:

2x

Next, we are adding fifteen:

2x + 15

a) After one second in the air, the cannonball's height is:

[tex]h = -16(1)^2 + 128(1) + 6 = 118 feet[/tex]

b) 8 seconds pass while the cannonball is in the air (from when it is fired until it hits the ground).

The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction. Its SI equivalent is the meter per second (ms-1). A body is considered to be accelerating if its velocity changes, either in magnitude or direction.

from the question:

a) We can enter values of t into the equation[tex]h = -16t^2 + 128t + 6[/tex] and evaluate to obtain the height of the cannonball each second after it is shot.

The height of the cannonball at time t = 0 is as follows:

[tex]h = -16(0)^2 + 128(0) + 6 = 6 feet[/tex]

When t = 1, the cannonball has been in the air for 1 second, so its height is:

[tex]h = -16(1)^2 + 128(1) + 6 = 118 feet[/tex]

b) The graph of the function [tex]h = -16t^2 + 128t + 6[/tex] can be used to calculate how long the projectile has been in the air. When the cannonball is six feet above the ground, it is said to be in the air. The values of t must be determined when h is larger than or equal to 6.

Finding the values of t where the graph crosses the line y = 6 is one technique to do this. Another is to graph the function. Another method is to solve for t while setting h = 6:

[tex]-16t^2 + 128t + 6 = 6[/tex]

[tex]-16t^2 + 128t = 0[/tex]

-16t(t - 8) = 0

t = 0 or t = 8

Hence, the cannonball flies for 8 seconds (from when it is fired until it hits the ground).

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Answer:

Approxiamaltely 91.95 feet

Step-by-step explanation:

The area of the composite figure is the sum of the area of the sector and the triangle . Therefore, the area of the composite figure is 95.52 cm².

This composite figure is created by placing a sector of a circle on a triangle. The area of the composite figure can be found as follows:

The composite figure is a combination of a sector and a right triangle. Therefore, the area of the composite figure is the sum of the area of the sector and the area of the right triangle.

area of the composite figure = area of the triangle + area of the sector

Hence,

area of the composite figure =  1 / 2 bh + ∅ / 360 × πr²

area of the composite figure = 1 / 2 × 6 × 8 + 82 / 360 × 3.14 × 10²

area of the composite figure = 48 / 2 + 25748 / 360

area of the composite figure = 24 + 71.5222222222

area of the composite figure = 95.5222222222

Therefore,

area of the composite figure = 95.52 cm²

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Answer:

10 cm

Step-by-step explanation:

Given:

A circular piece of paper of a radius of 20 cm is cut in half and each half is made into a hollow cone by joining the straight edges.

To find:

Find the slant height and base radius of each cone.

Solution:

The radius of the circular piece of paper = 20 cm

Finding the slant height of each cone:

Since the straight edges of the semi-circular part is joined together to form a cone

∴ Slant height of the cone so formed = Radius of the circular piece = 20 cm

Thus, the slant height of the cone is → 20 cm.

Finding the base radius of each cone:

Let "r" cm be the base radius of each cone.

We have,

[Length of the base of each cone] = [Length of each semi-circular part of the original circular piece of paper]

⇒

2

�

�

=

2

�

×

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

�

2

2πr=

2

2π × radius of original circle

⇒

2

�

=

2

×

20

2

2r=

2

2×20

⇒

2

�

=

20

2r=20

⇒

�

=

10

�

�

r=10cm

Thus, the base radius of each cone is → 10 cm.

If the car travels 160 miles, it will take approximately 2.7 hours to cover that distance.

An inverse function is a function that "undoes" the effect of another function. More specifically, if we have a function f(x), its inverse function g(x) will undo the effect of f(x), such that if we apply f(x) and then g(x) to an input x, we get back the original input.

To find the inverse function of d(t) = 60t, we need to solve for t in terms of d. We start by setting d equal to the original function and solving for t:

d = 60t

Dividing both sides by 60, we get:

t = d/60

So the inverse function is t(d) = d/60.

To find t(160), we substitute 160 for d in the equation t(d) = d/60:

t(160) = 160/60

t(160) = 2.67 (rounded to 1 decimal place)

Therefore, if the car travels 160 miles, it will take approximately 2.7 hours to cover that distance.

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1. We can see here that the modes of the given set of numbers will be: 12, 13, 14, 19.

2. The word in the sentence that is the mode is: the.

3. The mode of x is: 7

The mode of y is: - 2

In statistics, the mode is the value or values that occur most frequently in a given dataset. It is one of the most common measures of central tendency, along with the mean and the median.

To find the mode of a dataset, you need to look for the value that appears most often. If there is more than one value that occurs with the same highest frequency, the dataset is said to be bimodal or multimodal.

If no value appears more frequently than any other, the dataset is said to have no mode.

4. Modal class: 4-

Modal class: 12 - 20

5. Knowing the modal size of glass that its customers purchase can provide several benefits for the small company that sells glass. Here are some ways in which the company could benefit:

6. We can actually find the total frequency of the other three classes by subtracting the frequency of the first class from the total number of observations:

Total Frequency of the three classes = Total number of observations -Frequency of the first class

= 115 - 84 = 31

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Answer:

The answer is 25

The average rate of change of the number of farm²⁶ in the US between 1950 and 1970 would be = 8.3 farms/year

From the given graph above which shows the relationship between the number of farms and years. The line drawn from the origin shows an irregular relationship between the two variables.

The number of years between 1950 and 1970 = 20 years.

The number of farms that existed for those 20 years =5.2- 2.8 = 2.4 years

Therefore the average rate of change = 20/2.4 = 8.3 farms/year.

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Answer:

4/6 = 23

Step-by-step explanation:

The probability that the sum of the numbers when two dice are rolled is an odd number is given as follows:

0.5.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Each dice has six possible outcomes, hence the total number of outcomes when two dice are rolled is given as follows:

6² = 36.

When we look at the pattern of the sum of two dice, from (1,1), (1,2), ..., to (6,6) we see that they alternate between even numbers and odd numbers, hence:

Hence the probability is given as follows:

p = 18/36 = 0.5.

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The total surface area of the rectangular prism is 94 cm2.

Surface area is the measurement of the total area of a three-dimensional object. It is the sum of all the areas of the faces or surfaces of a 3D shape.

The total surface area of a 3D object is the sum of the areas of all its faces. The formula to calculate the total surface area of a 3D object is:

Total Surface Area = 2(Length x Width) + 2(Length x Height) + 2(Width x Height)

Where Length, Width, and Height are the dimensions of the 3D object.

For example, if you have a rectangular prism with Length = 5 cm, Width = 4 cm, Height = 3 cm, then the total surface area is:

Total Surface Area = 2(5 cm x 4 cm) + 2(5 cm x 3 cm) + 2(4 cm x 3 cm)

 = 40 cm2 + 30 cm2 + 24 cm2

 = 94 cm2

Therefore, the total surface area of the rectangular prism is 94 cm2.

In conclusion, the formula to calculate the total surface area of a 3D object is: Total Surface Area = 2(Length x Width) + 2(Length x Height) + 2(Width x Height). Examples can be used to better understand the concept and apply the formula to solve for the total surface area.

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The calculated volume of the prism with the dimension 6 1/2 cm by 2 1/2 cm by 2 1/2 cm is 325/8 cm³

To find the volume of a rectangular prism, we need to multiply its length, width, and height.

In this case, the length is 6 1/2 cm, the width is 2 1/2 cm, and the height is also 2 1/2 cm.

First, we need to convert the mixed numbers to improper fractions.

6 1/2 = 13/2

2 1/2 = 5/2

Now, we can multiply the three values together to find the volume:

Volume = length x width x height

Volume = (13/2) x (5/2) x (5/2)

Volume = (13 x 5 x 5) / (2 x 2 x 2)

Volume = 325/8

Therefore, the volume of the rectangular prism is 325/8 cm³

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The statement that must always be true fοr the median οf the triangle is RM = KM.

The statement that must always be true fοr the centrοid οf the triangle is RM = KM. Since, RM and KM are bοth part οf the median that cοnnect at the centrοid and are divided intο 2 halves.

A median in a triangle is a line segment that jοins οne οf the triangle's vertices tο the midway οf the οther side. There are three medians in every triangle, and they all cοme tοgether at the centrοid. The segment frοm the vertex tο the centrοid is twice as lοng as the segment frοm the centrοid tο the midpοint οf the οppοsing side.

The centrοid is the centre οf mass οf the triangle and splits each median intο twο segments. A median divides a triangle intο six smaller triangles οf equal size, passing thrοugh the centrοid οf each οf these smaller triangles, amοng οther nοtewοrthy qualities.

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Answer:

x-intercept(s):  

(

6

,

0

)

y-intercept(s):

(

0

,

−

9

)

Step-by-step explanation:

Given:-

To find:-

Solution:-

As we know that in a right angled triangle,

[tex]\implies \sin\theta =\dfrac{p}{h} \\[/tex]

And here;

On substituting the respective values, we have;

[tex]\implies \sin20^o = \dfrac{12}{x} \\[/tex]

[tex]\implies 0.342 =\dfrac{12}{x} \\[/tex]

[tex]\implies x = \dfrac{12}{0.342} \\[/tex]

[tex]\implies \underline{\underline{ x = 35.087}} \\[/tex]

Hence the value of x is 35.087 .

and we are done!

The length of the missing side of the given triangle above which is adjacent to angle 20° is 35.09.

To calculate the length of the missing side of the triangle, the formula given below is used. Such as:

Sin ∅ = opposite/hypothenuse.

Where ∅ = 20°

opposite = 12

hypotenuse = X

That is;

sin 20° = 12/X

make X the subject of formula;

X = 12/sin20°

X = 12/0.342020143

X = 35.09

Therefore the length of the missing part of the given triangle which is adjacent to angle 20° is 35.09.

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Hence, in answering the stated question, we may say that As a result, the  function mass of the 30 cm long PVC pipe is roughly 733.48 grammes, rounded to the nearest tenth.

Mathematicians investigate numbers and their variants, equations and associated structures, forms and their locations, and prospective locations for these things. The term "function" refers to the relationship between a group of inputs, each with its own output. A function is a connection of inputs and outputs in which each input results in a single, distinct outcome. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four basic types of accessible functions.

The volume of the PVC pipe can be estimated by subtracting the volumes of the outer and inner cylinders:

V = π/4 × (D² - d²) × L

where V denotes volume, is the mathematical constant pi (roughly equivalent to 3.14159), D denotes outer diameter, d denotes inner diameter, and L denotes pipe length.

V = π/4 × (6.5² - 5²) × 30\sV = 531.13 cm³

PVC pipe mass can be estimated by multiplying its volume by its density:

m = V × ρ

With the provided density, we get:

1.38 g/cm3 m = 733.48 g m = 531.13 cm3

As a result, the mass of the 30 cm long PVC pipe is roughly 733.48 grammes, rounded to the nearest tenth.

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The circumference of the circle is 144.44 yards

The circumference of a circle is the total distance around the edge of the circle. It's computed using the following formula:

Circumference = 2πr.

where r is the circle's radius and represents the ratio of a circle's circumference to its diameter by a mathematical constant π that roughly equals 3.14159.

We can also use the formula below whenever we have the diameter of the circle given

c = πd

where d is the diameter of the circle (the distance across the circle passing through the center).

From the image given, the circumference of the circle is given as;

c = 2πr

r = 23yd

c = 2 * 3.14 * 23

c = 144.44

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1. Have you taken a gap year in the past, or are you considering taking one in the future?

2. What do you think are the key benefits of taking a gap year?

3. Do you think taking a gap year is a beneficial educational experience?

4. Are there any downsides to taking a gap year, in your opinion?

5. What advice would you give to someone considering taking a gap year?

6. Do you think taking a gap year would provide skills/experiences that you couldn't gain elsewhere?

Answer:

The multiplication equation that shows how the denominators of 3/4 and 5/6 are related is:4 × 6 = 24To write an equivalent fraction with a denominator of 4, we need to find a number that, when multiplied by 4, gives us 24. That number is 6. So, we can multiply both the numerator and denominator of 3/4 by 6 to get:(3/4) × (6/6) = 18/2418/24 is equivalent to 3/4, but it has a denominator of 24 instead of 4. We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 6.(18/6) ÷ (24/6) = 3/4Therefore, the equivalent fraction of 3/4 with a denominator of 4 is 3/4 × 6/6 = 18/24, which simplifies to 3/4.

After answering the provided question, we can conclude that As a result, expression the likelihood that the sample mean book cost of 36 UCF students exceeds $1,278.6 is approximately 0.0427, or 4.27%.

In mathematics, an expression is a collection of symbols, digits, and companies that portray a statistical correlation or formula. An expression can be a single number, a mutable, or a combination of both of them. Addition, subtraction, proliferation, division, and exponentiation are examples of mathematical operators.  Expressions are used extensively in mathematics, including arithmetic, calculus, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification. \

[tex]P(x > 1278.6) = P(z > (1278.6-1245)/(102/36)) P(z > 1.72) = 0.0427 P(z > 1.72) = 0.0427[/tex]

As a result, the likelihood that the sample mean book cost of 36 UCF students exceeds $1,278.6 is approximately 0.0427, or 4.27%.

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