x is proportional to the square root of y, where y > 0

y is increased by 44%

Work out the percentage increase in x

The height of the tree is 60 ft

Proportion is defined as as an equation that is made equal to another

From the information given, we have that;

The shadow casted by the tree = 30 ft

The height of the pole = 6ft

The shadow casted by the pole = 3ft

Then, we have that;

If 6ft = 3ft

xft = 30ft

cross multiply the values, we have;

3x = 30(6)

Multiply the values

3x = 180

Divide both sides by the coefficient of the variable

x = 60ft

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Answer:

[tex]\bold{V=7048.48 ft^3}[/tex]

Step-by-step explanation:

Solution Given:

radius(r)=12

In right-angled triangle

Hypotenuse = 18

base angle =60°

Note:
In a right-angled triangle, we can use the trigonometric ratios sine, cosine, and tangent to relate the angles and sides of the triangle.
Here are the trigonometric ratios for a right-angled triangle:

Sine (sin): The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

[tex]\boxed{\bold{sin(A) =\frac{ opposite}{hypotenuse}}}[/tex]

Cosine (cos): The cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

[tex]\boxed{\bold{cos(A) = \frac{adjacent}{hypotenuse}}}[/tex]

Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

[tex]\boxed{\bold{tan(A) =\frac{ opposite}{adjacent}}}[/tex]

Now for the question:

Over here the relation between opposite or height and hypotenuse is given by Sine, So using this formula:

[tex]\bold{sin(60^0) =\frac{ opposite\:or\ height}{18}}[/tex]

doing criss-cross multiplication:

Sin 60°*18=opposite or height

[tex]\frac{\sqrt{3}}{2}*18[/tex] =opposite or height

opposite or height(h)=[tex]9\sqrt{3}[/tex]

Again,

We have

[tex]\boxed{\bold{Volume\:of\:cylinder= \pi * r^2 * h}}[/tex]

where:

π (pi) is a mathematical constant approximately equal to 3.14

r is the radius of the base of the cylinder

h is the height of the cylinder

Now Substituting value

[tex]Volume = \pi * r^2 * h\\Volume=3.14*12^2*9\sqrt{3}\\Volume=\bold{7048.48 ft^3}[/tex]

Answer:

[tex]C = 25.1 \text{ cm}[/tex]

Step-by-step explanation:

We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:

[tex]C = \pi d[/tex]

Note: This formula can also be written as [tex]C = 2\pi r[/tex] because [tex]2r = d[/tex].

↓ plugging in the given radius

[tex]C = 8\pi \text{ cm}[/tex]

↓ rounding to the nearest tenth

[tex]\boxed{C = 25.1 \text{ cm}}[/tex]

Answer: $89 for one day and 70 miles

Step-by-step explanation:

The correct probability from the two-way table is given as follows:

B. P(120 lb | 2,000 - 2,500 cal) is different of P(120 lb).

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.

Then the probabilities are given as follows:

Hence statement B is true.

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The correct answer to the fraction task is 3/5 + 1/2 = 11/10 expressed as a fraction and 4/7 is incorrect answer

The pupil made an error in their addition of 3/5 and 1/2, resulting in an incorrect answer of 4/7.

To solve the task correctly, we need to find a common denominator for 3/5 and 1/2.

The least common multiple of 5 and 2 is 10, so we can rewrite the fractions with a denominator of 10 as follows:

3/5 = 6/10

1/2 = 5/10

Now we can add the fractions:

6/10 + 5/10 = 11/10

Hence, the correct answer to the fraction task is 3/5 + 1/2 = 11/10 expressed as a fraction.

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H contains the identity element, is closed under multiplication, and is closed under taking inverses, H is a subgroup of G, as desired.

Let [tex]\mathcal{H}[/tex]  be a non-empty directed family of subgroups of a group G. We need to show that the union [tex]H=\bigcup_{H_i\in\mathcal{H}}H_i[/tex] is a subgroup of G.

First, note that H is non-empty since[tex]\mathcal{H}[/tex] is non-empty. We also have [tex]1_G \in H_i[/tex] for all [tex]H_i\in\mathcal{H}[/tex], so [tex]1_G \in H.[/tex]

To show that H is closed under multiplication, let [tex]h_1,h_2\in H[/tex]. Then there exist [tex]H_{i_1},H_{i_2}\in\mathcal{H}[/tex] such that [tex]h_1\in H_{i_1}[/tex] and [tex]h_2\in H_{i_2}.[/tex] Since [tex]\mathcal{H}[/tex] is directed, there exists[tex]H_{i_3}\in\mathcal{H}[/tex] such that [tex]H_{i_1}\cup H_{i_2} \subseteq H_{i_3}[/tex]. Thus, [tex]h_1,h_2\in H_{i_3},[/tex]and since [tex]H_{i_3}[/tex] is a subgroup, we have [tex]h_1h_2\in H_{i_3} \subseteq H[/tex]. Therefore, H is closed under multiplication.

Finally, to show that H is closed under taking inverses, let h\in H. Then there exists [tex]H_i\in\mathcal{H}[/tex] such that [tex]h\in H_i[/tex]. Since [tex]H_i[/tex]is a subgroup, we have [tex]h^{-1}\in H_i \subseteq H[/tex]. Therefore, H is closed under taking inverses.

Since H contains the identity element, is closed under multiplication, and is closed under taking inverses, H is a subgroup of G, as desired.

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The solution to the equation when solved for m is  (v - e)/Z.

To solve for m in the equation Z = (v - e)/m, we can manipulate the equation algebraically as follows:

Z = (v - e)/m

Multiply both sides by m:

Zm = v - e

Add e to both sides:

Zm + e = v

Subtract e from both sides:

Zm = v - e

Divide both sides by Z:

m = (v - e)/Z

Therefore, the solution for m is:

m = (v - e)/Z.

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Answer:

Step-by-step explanation:

For Company C, the total cost in dollars, denoted as t, can be calculated using the following equation:

t = 27n + 18

In this equation, 27n represents the cost of the bracelets (charging $27 per bracelet), and 18 represents the flat rate for shipping any number of bracelets. By summing these two components, we obtain the total cost of the friendship bracelets from Company C in terms of the number of bracelets, n.

After considering the given details we conclude that the height of the picture frame is 12, under the condition that the diagonal of a picture frame is 18 inches the base of the picture frame is 12.

The height of the picture frame can be evaluated applying  the Pythagorean theorem. The Pythagorean theorem projects that in a right triangle, the square of the length of the hypotenuse (the diagonal of the picture frame) is equivalent to the summation of the squares of the lengths of the other two sides (the height and base of the picture frame).

Therefore , in this case, we have a right triangle with a hypotenuse of 18 inches and a base of 12 inches. We can evaluate for the height as follows:
height²+ 12² = 18²
height² = 18² - 12²
height² = 144
height = √(144)
height = 12
Hence, the height of the picture frame is 12 inches rounded to the nearest tenth.
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The corresponding angles and sides that show that the triangles are similar are: <A ≅ <R; <K ≅ <T; <M ≅ <L

RL/AM = RT/AK = TL/KM = 1.5.

Similar triangles are triangles that look alike but might be bigger or smaller than each other. This means that their matching or corresponding angles are the same and their matching sides have the same proportional length.

Therefore, from the image, we have corresponding pairs of angles that are congruent as follows:

Angles A and R

Angles K and T

Angles M and L

The corresponding sides that are proportional are:

AM and RL, which is RL/AM = 6/4 = 1.5

AK and RT, which is RT/AK = 7.5/5 = 1.5

KM and TL, which is TL/KM = 9/6 = 1.5

Therefore, the triangles are similar.

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Answer:

1761 ft²

Step-by-step explanation:

The shape of the attic is a triangular prism.

It has 5 faces: The bases are 2 faces that are congruent triangles. The other 3 faces are rectangles, 2 of which are congruent.

surface area = area of the bases + area of 3 rectangles

surface area = 2 × area of triangle + 2 × area of rectangle + area of other rectangle

surface area = 2 × (1/2)bh + 2 × length × width + LENGTH × WIDTH

surface area = 2 × (1/2)(15 ft)(15 ft) + 2(15 ft)(30 ft) + (21.2 ft)(30 ft)

surface area = 225 ft² + 900 ft² + 636 ft²

surface area = 1761 ft²

The earthquake registered 3.6 on the Richter scale.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is given as follows:

R = log(A/0.0001)

The amplitude of the earthquake was of 0.3954, hence the magnitude of the earthquake is obtained as follows:

R = log(0.3954/0.0001)

R = 3.6.

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The line of the best fit that models the data is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The graph

To draw a line to model the data is to draw the line of best fit

A good line of best fit would have equal number of points on either sides

To plot the graph, we draw a line that divides the points on the graph evenly

This line when drawn on the scattered points divided the points approximately evenly

Hence, the line of the model is attached

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Answer:

32) (x+12)(2)+(y)(2)=25

Step-by-step explanation:

(x-a)(2)+(y-b)(2)=r(2)

(x-(-12)(2)+(y-0)(2)=5(2)

(x+12)+(y)=25

Answer(s):

(32) - [tex](x +12)^2 + y ^2 = 25[/tex]

(33) - [tex](x +2)^2 + (y+6 )^2 = 36[/tex]

(34) - [tex](x -8)^2 + (y+1 )^2 = 100[/tex]

(35) - [tex](x -13)^2 + (y+12 )^2 = 1[/tex]

Step-by-step explanation:

To solve these types of problems, it is only a matter of memorizing the equation of a circle and plugging in values appropriately.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{The Equation of a Circle:}}\\\\(x - h)^2 + (y - k)^2 = r^2\\\text{Where} \ r \ \text{is the radius of the circle and} \ (h,k) \ \text{is the center of the circle.}\end{array}\right}[/tex]

For the following problems, find the equation of a circle with the given information.

(32) - [tex]\text{Center at} \ (-12,0) \ \text{and a radius,} \ r=5[/tex]

(33) - [tex]\text{Center at} \ (-2,-6) \ \text{and a radius,} \ r=6[/tex]

(34) - [tex]\text{Center at} \ (8,-1) \ \text{and a radius,} \ r=10[/tex]

(35) - [tex]\text{Center at} \ (13,-12) \ \text{and a radius,} \ r=1[/tex]

Question #32:

[tex](x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - (-12))^2 + (y - 0)^2 = (5)^2\\\\\Longrightarrow \boxed{ (x +12)^2 + y ^2 = 25}[/tex]

Question #33:

[tex](x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - (-2))^2 + (y - (-6))^2 = (6)^2\\\\\Longrightarrow \boxed{ (x +2)^2 + (y+6 )^2 = 36}[/tex]

Question #34:

[tex](x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - 8)^2 + (y - (-1))^2 = (10)^2\\\\\Longrightarrow \boxed{ (x -8)^2 + (y+1 )^2 = 100}[/tex]

Question #35:

[tex](x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - 13)^2 + (y - (-12))^2 = (1)^2\\\\\Longrightarrow \boxed{ (x -13)^2 + (y+12 )^2 = 1}[/tex]

Thus, all problems have been solved.

Answer:

a] 24.5; b] 2.8; c] 39.59.

Step-by-step explanation:

a. after t=1sec:

h(1)=-4.9*1²+27*1+2.4; ⇔h(1)=24.5 [m];

b. more than 30 [m] heigh:

-4.9t²+27t+2.4≥30; ⇔ 4.9t²-27t+27.6≤0; ⇔(t-1.35)(t-4.15)≤0;

Δt≈4.15-1.35=2.8 [sec];

c. maximum height:

h'(t)=-9.7t+27; ⇒ h'(t)=0, ⇒ -9.7(t-2.78)=0; ⇒ t=2.78 [sec], then

[tex]h_{max}=h(2.78)=-4.9*2.78^2+27*2.78+2.4=39.59[m].[/tex]

Answer:

y = [tex]\frac{25x+22}{6}[/tex]

Step-by-step explanation:

express the ratios in fractional form

[tex]\frac{5x+2}{y-2}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )

6(y - 2) = 5(5x + 2) ← distribute parenthesis on both sides

6y - 12 = 25x + 10 ( add 12 to both sides )

6y = 25x + 22 ( divide both sides by 6 )

y = [tex]\frac{25x+22}{6}[/tex]

Answer: x= 3

Step-by-step explanation:

We solve the given equation to obtain value of x

Step 1: We open the bracket:

8x-6-8=4+2x

Step 2: We transform terms with x to left hand side and constants to the right hand side and change their signs

8x-2x=4+6+8

6x=18

x=18/6

Thus, x=3

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Jeremy is wrong as I explained below.

As we know,

Thus, as we can see from the figure figure 1 is a rectangle and Figure 2 is a square so,

I do not agree with Jeremy.

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Complete question:

The interest Pedro will have to pay is $5200

From the question, we have the following parameters that can be used in our computation:

Principal = $32.500

Rate = 4% simple interest

Time = 4 years

The formula of simple iinterest is

I = Principal * Rate * Time

substitute the known values in the above equation, so, we have the following representation

I = 32500 * 4% * 4

Evaluate

I = 5200

Hence, Pedro have to pay $5200 as interest

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Answer:

4.81 × 10-1

Also its "write"

Also I have your IP

Also I'm kidding relax

The range is 5 years.The median is 18 years.

To determine the range and median from the given dot plot of ages, we need to analyze the distribution of the data points.

The range represents the difference between the maximum and minimum values in a dataset. Looking at the dot plot, the minimum age appears to be 16, while the maximum age is 21. Therefore, the range can be calculated as:

Range = Maximum age - Minimum age = 21 - 16 = 5 years.

Thus, the range of the ages of employees at the summer camp is 5 years.

The median represents the middle value in a dataset when it is arranged in ascending or descending order. To determine the median, we need to organize the ages in order from least to greatest:

16, 17, 18, 19, 20, 21

Since there are six data points, the median would be the value in the middle. In this case, the median would be the third value, which is 18.

Therefore, the median of the ages of employees at the summer camp is 18 years.

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The decimal that represents the number of packs of loom bands that Natalie has is 7.57.

We can see that Natalie has 7 full packs of loom bands, which is a total of:

7*100= 700 loom bands

In addition, she has 57 other bands, making a total of:

700+57 =757 loom bands.

Now to find the decimal that represents the number of packs Natalie has, we need to divide the total number of loom bands by 100, since there are 100 bands in each pack. Thus, we have:

757 / 100 = 7.57

Therefore, the decimal that represents the number of packs of loom bands that Natalie has is 7.57.

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Answer:

The volume of the figure is 76ft³.

Step-by-step explanation:

Divide the figure into 2 parts to make it easier to solve for the volume.

V1 = 6ft(2ft)(3ft)

V1 = 36ft³

V2 = 4ft(2ft)(5ft)

V2 = 40ft³

V = V1 + V2

V = 36ft³ + 40ft³

V = 76ft³

In this question, measure of angle 4 is c. 60 degree. It has been calculated using properties of parallel lines.

It can be seen that in this question l and m are parallel lines and there is a transverse passing through it. We know through the properties of parallel lines that sum of ∠2 and ∠4 is 180° as they are consecutive interior angles and consecutive interior angles are supplementary meaning their sum is 180.

∠2 + ∠4 = 180° (consecutive interior angles)

120° + ∠4 = 180°

∠4 = 180 - 120

= 60°

Parallel lines are straight lines that never meet, no matter how far they are extended. Many pairs of angles are generated when two parallel lines are intersected by another line known as a transversal.

Some angles are congruent (equal), whereas others are supplementary (different).  Consecutive interior angles, also known as co-interior angles, develop on the inside of the transversal and are additional.

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Answer:

[tex]\sf g(x) = f(x\; \boxed{+ 3}\;) \;\boxed{- 6}[/tex]

Step-by-step explanation:

A translation is a transformation that moves every point of a figure the same distance and in the same direction. This means that the size, shape, and orientation of the figure are preserved, but its position is changed.

From inspection of the given diagram, we can see that the size, shape and orientation of the graph of function g is the same as that of the graph of function f, but its position has changed.  Therefore, the transformation is a translation.

We can use the vertex of both graphs to determine the translation.

Therefore, the graph of function f has been moved 3 units left and 6 units down to create the graph of function g.

When we move "a" units left, we add the value of "a" to the x-value of the function.

When we move "a" units down, we subtract the value of "a" from the function.

Therefore:

[tex]\sf g(x) = f(x\; \boxed{+ 3}\;) \;\boxed{- 6}[/tex]

Answer:

43.07

Step-by-step explanation:

remove the decimals and divide them as whole numbers then after the successful division return the decimal places according to the number of decimal places in each that is minus the number of decimal places in the divisor from the numbers of decimal places in the dividend

In order to convert the base of the logarithm from base 10 to any other base and calculate intensities, we need the change of base formula.

To solve this problem, we need to use the logarithmic property known as the "change of base formula" which states that:

log_a (b) = log_c (b) / log_c (a)

This formula allows us to change the base of a logarithm from one value to another.

In this case, we want to find the ratio of the intensity of the first speaker to that of the second speaker, which is given by:

ratio = intensity of the first speaker/intensity of the second speaker

To calculate this ratio, we need to first convert the decibel values to intensities using the formula:

intensity = 10^(dB/10)

where dB is the decibel value.

For the first speaker, the intensity is:

intensity of the first speaker = [tex]10^{(85/10)} = 7.94 *10^8[/tex]

For the second speaker, the intensity is:

the intensity of the second speaker [tex]= 10^{(75/10)} = 1.78 * 10^7[/tex]

Now we can calculate the ratio of intensities:

[tex]ratio = (7.94 * 10^8) / (1.78 * 10^7) = 44.66[/tex]

This means that the sound from the first speaker is 44.66 times more intense than the sound from the second speaker.

Therefore, we need the change of base formula to change the base of the logarithm from 10 to any other base to calculate the intensities.

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It is important to note that this equation assumes a constant density of seawater, which is not always the case in the deep ocean. In addition, the pressure at a given depth can vary depending on factors such as temperature and salinity. This equation should be used with caution and in conjunction with other measurements and data analysis techniques.

The given equation for pressure in pounds per square foot at a depth of d feet is P = 14 + 4d/9. We are given that the pressure measured by the scientific team is 306 pounds per square foot. To find the depth at which this pressure is measured, we need to solve the equation for d.

Substituting P = 306 in the equation, we get:

306 = 14 + 4d/9

Multiplying both sides by 9, we get:

2754 = 126 + 4d

Subtracting 126 from both sides, we get:

2628 = 4d

Dividing both sides by 4, we get:

d = 657 feet

The scientific team is measuring the pressure at a depth of 657 feet below the surface of the ocean.

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