4. Circle O is shown below. The diagram is not drawn to scale.

The value of p is equal to 76 when q is equal to 4

Given :

If p is inversely proportional to the square of q

when y is inversely proportional to x then [tex]y=\frac{k}{x}[/tex]

given that p is inversely proportional to the square of q. the equation becomes

[tex]p=\frac{k}{q^2}[/tex]

when p is 19 the value of a is 8

Replace the values and find out q

[tex]p=\frac{k}{q^2}[/tex]

[tex]22=\frac{k}{8^2}[/tex]

[tex]22=\frac{k}{64}[/tex]

Multiply both sides by 64

k=1216

Now we find out p when q is 4

Replace k value and q value to find out p

[tex]p=\frac{k}{q^2}[/tex]

[tex]p=76[/tex]

The value of p is equal to 76 when q is equal to 4

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Answer:

P = 88.

Step-by-step explanation:

P = k/q^2

22 = k/ 8^2

k = 22 * 64 = 1408.

So P = 1408/q^2

When q = 4:

P = 1408/4^2

q = 88

Answer:

3/5+1/3= 9/15+5/15= 14/15

Step-by-step explanation:

Hi there!

To make fractions have a common denominator, multiply both the numerator and the denominator by a number. In this case, 3/5= 9/15, because both the numerator and denominator are multiplied by 3. 1/3= 5/15, using the same rule. 9/15+5/15=14/15

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Answer:

mode

is the most common frequent value

Answer:

The Third Angle theorem is not enough to prove that two triangles are congruent.

Step-by-step explanation:

It establishes that if two angles of one triangle are congruent with two angles of another triangle, then the third angles are also congruent. This indicates that the two triangles are similar but not identical.

There are 10 number of 1 cubic inches box required to fill the container completely.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape.

We have:

A prism with a length of 4 inches, height of 4 inches, and width of 3 inches.

The volume of the prism box = 4×4×3 = 48 cubic inches

Here some data are missing.

We are assuming there are 38 1 cubic inches box already in the big box.

So,

= 48 - 38

= 10

Thus, there are 10 number of 1 cubic inches box required to fill the container completely.

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Step-by-step explanation:

got the answer see in the image :)

Answer:

[tex]2\frac{1}{5}[/tex]

Step-by-step explanation:

The 11 gals of water are equally split up into 5 tanks, so divide 11 by 5.

[tex]\frac{11}{5}[/tex] then simplifies into [tex]2\frac{1}{5}[/tex]

Answer:

see explanation

Step-by-step explanation:

the equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 9 ← is in this form

with centre (0, 0 ) and r = [tex]\sqrt{9}[/tex] = 3

this then is the equation of a circle whose centre is (0, 0 ) with radius 3

Answer:

Step-by-step explanation:

Discussion

Answer:

it's not reasonable because the t-shirts alone cost 30 and the shoes cost 20 so it would cost 50 altogether.

Answer:

290 in^2.

Step-by-step explanation:

Adding all the areas of rectangles:

= 11*8 + 11*3 + 11*8 + 11*3 + 3*8 + 3*8

= 290 in^2.

Answer:

B)  290 in²

Step-by-step explanation:

Area of a rectangle = length × width

⇒ SA of the net = 2(11 × 8) + 2(11 × 3) + 2(8 ×3)

                           = 176 + 66 + 48

                           = 290 in²

Answer:

the answer is A. sorry for dirty handwriting

Answer:

h=52 and h is the shortest

Step-by-step explanation:

180-f-g=h    step 1. -f from 180

180-60=120   step 2. -g from 120

120-68= 52

h=52 degrees

Answer:

x = -14

Step-by-step explanation:

Divide each side by -3.

Subtract 9 from each side.

Answer:

x = -14

Step-by-step explanation:

-3(x + 9) = 15

Answer:

for "A" the answer is 247$

For "B" the answer 11 hours

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

4 layers 15 cubes

the total amount of cubes =5*3*4

Answer:

See below ~

Step-by-step explanation:

Completing the square :

Graph :

Answer:

x = 9(y - 1)² + 1

see attached for graph

Step-by-step explanation:

Given equation:

9y² - x - 18y + 10 = 0 ​

As there is a y² in the equation, this implies it is a sideways parabola.

To complete the square for a sideways parabola, collect the y variable terms on the left and everything else on the right:

⇒ 9y² - 18y = x - 10

Factor out the leading coefficient from the left side:

⇒ 9(y² - 2y) = x - 10

Take the coefficient of y, half it, then square it:  (-2 ÷ 2)² = 1

Add this inside the parentheses, and add the distributed value of this to the right side:

⇒ 9(y² - 2y + 1) = x - 10 + 9

Factor the parentheses and simplify the right side:

⇒ 9(y - 1)² = x - 1

Add 1 to both sides to make x the subject:

⇒ x = 9(y - 1)² + 1

Conic form of a sideways parabola with a horizontal axis of symmetry:

x = a(y - k)² + h

(where (h, k) is the vertex and y = k is the axis of symmetry)

If a > 0, the parabola opens to the right, and if a < 0, the parabola opens to the left.

Therefore, for  x = 9(y - 1)² + 1

To find the x-intercept, set y = 0 and solve for x:

⇒ x = 9(0 - 1)² + 1

⇒ x = 9(-1)² + 1

⇒ x = 9(1) + 1

⇒ x = 10

Therefore, the y-intercept is (10, 0)

As the axis of symmetry is y = 1, the other value of y when x = 10 is y = 2

Plot the vertex and points. Add an axis of symmetry to help draw the curve.  Draw the parabola opening to the right.

**graph attached**

Answer:

9.5 feet

Step-by-step explanation:

Area of square garden = side length²

⇒ 90 = l²

⇒ l = √90

⇒ l = 3√10

⇒ l = 9.5 feet (nearest tenth)

The length of one side lies between the whole numbers 9 and 10.

Answer:

9 and 10

side length = 9.5 ft (nearest tenth)

Step-by-step explanation:

Area of a square = s²  (where s is the side length)

Therefore, if the square garden measures 90 ft², the length of one side will be √90.

To find the two whole numbers that √90 lies between, find the perfect square either side of 90.

Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, ...

Therefore, 90 lies between 81 and 100:  

⇒ 81 < 90 < 100

Square root the numbers:

⇒ √81 < √90 < √100

⇒ 9 < √90 < 10

Therefore, the length of one side of Grandma's garden is between 9 and 10.

To estimate √90 to the nearest tenth, find the difference between the three numbers:

[tex]81 \overset{+9}{\longrightarrow} 90 \overset{+10}{\longrightarrow} 100[/tex]

As 90 is almost in the middle of 81 and 100,

⇒ √90 = 9.5 (nearest tenth)

According to the calculator, √90 = 9.486832981... = 9.5 (nearest tenth)
which verifies the estimation.

Using it's formula, it is found that the accuracy of the test was of 0.85 = 85%.

The accuracy of a test is given by the number of correct results divided by the number of results.

In this problem, there are 80 tests, and of those, 5 + 7 = 12 had incorrect results, hence 68 had correct results.

Hence the accuracy of the test is given by:

a = 68/80 = 0.85 = 85%.

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Answer:

a = 337.214 m2

Step-by-step explanation:

hope this helps

As tangents from a single point to the circle are equal in measure

ABC is isosceles

<A=60°

We know the radius hits any tangent on right angles

So

Now

accurate value

Answer:

[tex]x=4\sqrt{3}[/tex]

Step-by-step explanation:

If two tangents to a circle meet at one exterior point, the tangent segments are congruent.   Therefore, AC = BC

This means that ΔABC is an isosceles triangle and so
∠ABC = ∠BAC = 60°

The tangent of a circle is always perpendicular to the radius.

Therefore, ∠PAC = 90°

With this information, we can calculate ∠PAD:

⇒ ∠PAD + ∠BAC = ∠PAC

⇒ ∠PAD + 60° = 90°

⇒ ∠PAD = 90° - 60°

⇒ ∠PAD = 30°

We now have a side length and an angle of ΔPAD (shown in orange on the attached diagram).  So using the cos trig ratio, we can calculate [tex]x[/tex]:

[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]

where:

Given:

[tex]\implies \cos(30^{\circ})=\dfrac{6}{x}[/tex]

[tex]\implies x=\dfrac{6}{\cos(30^{\circ})}[/tex]

[tex]\implies x=\dfrac{6}{\frac{\sqrt{3}}{2}}[/tex]

[tex]\implies x=4\sqrt{3}[/tex]

A simple random sample from an infinite population is a sample selected such that each element is selected independently and from the same population.

Simple random sampling is known to be a  types of sampling where there are no laws, rules etc., on how to select the samples.

Note that it is seen easiest way of sampling and as such, A simple random sample from an infinite population is a sample selected such that each element is selected independently and from the same population.

See full question below

A simple random sample from an infinite population is a sample selected such that:

a. each element is selected independently and from the same population

b. each element has a 0.5 probability of being selected

c. each element has a probability of at least 0.5 of being selected

d. the probability of being selected changes

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Answer:

C) cross products

Step-by-step explanation:

Let's say you were solving [tex]\frac{1}{2}=\frac{x}{4}[/tex] for example. You would need to use cross products to simplify the problem. Here, the left side would be 1*4, and the right side would be 2*x, giving you [tex]4=2x[/tex], thus, leading to the solution [tex]x=2[/tex]. We can see clearly that the cross products would thus need to be equal to each other.

Answer:

The population was 600 in 1968

Step-by-step explanation:

The population of an island decreased by 40% over 50 years, so the population in 1968 will be equal to 600.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

As per the data provided by the question,

The current population in 2018 = is 360

which is 40% less than the population in 1968.

So, 60% of the total population will be equal to 360.
Let the total population is x.

60% × x = 360

x = (360 × 100)/60

x = 600

Therefore, the population at that time was 600.

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Answer:

1/2

Step-by-step explanation:

number of required outcome ÷number of possible outcomes

1/2

Answer:

For #14, (around) 108 times.

#15 = 53

Step-by-step explanation:

14)

2.69*10^5 = 269000

2.5*10^3 = 2500

269000/2500 = 107.6

Rounding up, we get 108

15)

√(53 - 8)2 + (31 - 3)2

= √(45)2 + (28)2

= √2809

= 53

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Answer:

99 in³

Step-by-step explanation:

Let the radius and height of each be r and h in. respectively.

Write an equation for the volume of cone.

Volume of cone= ⅓πr²h

⅓πr²h= 33

Multiply both sides by 3:

πr²h= 99

Volume of cylinder= πr²h

We have found the value of πr²h previously, which is 99.

Thus, the volume of the cylinder is 99 in³.