Find the smallest number by which 1008 must be multiplied to get a perfect square. also, find the square root of the perfect square so obtained

The figure that is not equivalent to 2¾ is 2¼ × 2½. That is option B.

Simplification is a process that is used to make a fraction appear in its simplest forms.

The fraction given is = 2¾

The simplification of the fraction= 2^3/4 = 2

But simplification of 2¼ × 2½ is equal to;

2¼= 0.5

2½= 1

Therefore 2¾ is not equivalent to 2¼ × 2½ when simplified.

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Answer:

The file contains the solution to the above question

Ryan's data collection is true that Ryan did a survey  he asked about qualitative data.

Given that Ryan called every school in the district to find out if they had a recycling program.

We know that there are two types of data:

Quantitative data deals with numbers and things that we can count or measure such as dimensions such as height, width, and length.

Qualitative data relating to characteristics and descriptions cannot be counted or measured, but are observable by their qualities such as smell, taste, and color.

If we ask for quantitative data, the survey will be quantitative. Data recycling means the quality of the data available.

They can ask for a yes or no answer, as in the Ryan investigation.

Hence, the correct statement about Ryan's data collection is: Ryan conducted a survey in which he asked about qualitative data.

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Answer:

Step-by-step explanation:

you are right AC is 16 because A-C are the same length

The true statement regarding the graphed function is that f(-2) = g(-2).

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given is a graphed function.

The graph contains two functions f(x) and g(x).

From the graph, it is clear that,

The two graphs intersect at a certain point, where the both functions passes through.

The intersecting point is (-2, 4).

This point can be written as (-2, f(-2)) and (-2, g(-2)).

This implies that,

f(-2) = g(-2)

Hence the true statement is f(-2) = g(-2).

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Your question is incomplete. The complete question is as given below.

Answer:

41 yards by 118 yards

Step-by-step explanation:

Let W and L be the Width and Length of the playing field:

The perimeter, P, would be P = 2W + 2L

We are told that P = 318 yards.

We learn that L = 3W - 5

Combining this information, we can say:

P = 2W + 2L                         [Oriinal equation]

318 = 2W + 2L                      [P is 318]

318 = 2W + 2(3W-5)             [ Use the definition of L = 3W - 5]

318 = 2W + 6W - 10

328 = 8W

W = 41 yards

Use this value of W to find L:

L = 3W - 5

L = 3(41) - 5

L = 123 - 5

L = 118

CHECK

Does 2*(118) + 2*(41) = 318?  YES

Is the length 5 yards less than triple the width?

3*(41) - 5 = 118  YES

Answer: 1800

Step-by-step explanation:

Exterior angles of a polygon add to 360 degrees, so this means the polygon has 12 sides.

We also know that since an interior angle and its corresponding exterior angle are supplementary, each interior angle is 150 degrees.

Therefore, the sum of the measures of the interior angles is (150)(12)=1800 degrees.

The characteristic of certificates of deposit (CDs) is that it last for a set period of time and is denoted as option B.

This is also referred to as time deposit and is characterized by a lump sum being saved at a fixed period of time and is stricter than the normal savings system.

This type of savings has a fixed interest rate and can't be withdrawn before the maturity date unlike savings account which can be accessed at any point in time which makes it unique and is therefore the most appropriate choice.

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If a semicircle is rotated about the x axis of the graph then the resulting three dimensional shape will be a sphere.

Given a semicircle on a graph.

A semicircle is a half circle .A sphere is a geometrical object that is a three dimensional  shape , It is the set of points that are all at the same distance r from given point in three dimensional shape.

Rotation is basically an action of rotating around an object or an axis.

If a semicircle is rotated about x axis then the resulting figure will be a sphere. This is because of the fact that when the semi circle is rotated about the x axis then all the points will be at equal distance in all directions from the center.

Hence if a semicircle is rotated about x axis then the resulting figure will be a sphere.

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Answer:

13.4 or √180

Step-by-step explanation:

Pythagorean theorem states

a² + b² = c²

C^2 is the longest side. The corner of the right angle points to it. The other sides are your a and b squared. They are called the legs or Opposite and Adjacent sides.

Answer: S ≈ 48.2°

Step-by-step explanation:

   We can use trigonometry functions to solve.

   Looking at angle S, t = 18 is the hypotenuse and r = 12 is the adjacent side. This means we can use the cosine function.

   [tex]\displaystyle cos(S) = \frac{\text{adjacent side}}{\text{hypotenuse }}=\frac{12}{18}[/tex]

  [tex]\displaystyle cos^{-1} (cos(S)) = (\frac{\text{adjacent side}}{\text{hypotenuse }}=\frac{12}{18})cos^{-1}[/tex]

  [tex]S = 48.189685...\\S \;$\approx$\; 48.2^{\circ}[/tex]

Answer:

AC = 10

Step-by-step explanation:

Formula

(x + 1) + (x + 3) + 2x = 40                Remove the brackets

Solution

x + 1 + x + 3 + 2x = 40                    Collect like terms

4x + 4 = 40                                     Subtract 4 from both sides

4x +4 -4 = 40 - 4                             Combine

4x = 36                                            Divide both sides by 4

4x/4 = 36/4

x = 9

AC = x + 1

AC = 9 + 1

AC = 10

Based on the calculations, the magnitude of m∠EFH is equal to 112°.

In Geometry, the sum of two (2) non-adjacent interior angles in a triangle is equal to its exterior angle. Thus, we have:

(3x - 3) + 76 = 8x + 8

3x + 73 = 8x + 8

73 - 8 = 8x - 3x

65 = 5x

x = 65/5

x = 13.

From triangle GFH, we have:

m∠EFH = ∠F = 8x + 8

m∠EFH = 8 (13) + 8

m∠EFH = 104 + 8

m∠EFH = 112°.

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The value of x in the equation 1 1/5 - x/3 = 9/10 is 9/10

1 1/5 - x/3 = 9/10

- x/3 = 9/10 - 1 1/5

- x/3 = 9/10 - 6/5

-x/3 = 9-12 / 10

-x/3 = -3/10

x = -3/10 ÷ - 1/3

= -3/10 × -3/1

x = 9/10

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A data value is considered significantly low or significantly high  if its​ z-score is less than -2 or greater than 2.

What does it mean if z-score is 2?

What does a standard deviation of 2 mean?

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The correct question is -

A data value is considered​ _______ if its​ z-score is less than minus−2 or greater than 2.

The angle formed at J and the angle of elevation at L are alternate angles, such that the angle of elevation is 53°

The given parameters are;

Triangle ∆JKL is a right triangle

The slope of the line LJ = Positive

The angle formed by the horizontal line at J = 53°

Required;

The angle of elevation from point L to point J

Solution;

The angle of elevation at L is formed by an horizontal line drawn at L.

The two horizontal lines are parallel, and the angle of elevation at L is the alternate angle to the angle formed by the horizontal line at J.

Given that alternate angles formed between parallel lines having a common transversal are equal, we have;

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Answer:

C. 53 degrees

Step-by-step explanation:

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The distance at which pumpkins are the same height.

What do you mean by X and Y coordinates?

The X and Y coordinates are an address that help locate a point in two dimensions of space. The coordinates (x, y) are used to represent any point in the coordinate plane. The x value indicates the point's position in regard to the x-axis, and the y value indicates its position in relation to the y-axis.

Both equations' graphs would be at an intersection, which would indicate that their x and y coordinates are identical. The same y coordinate would indicate being at the same height at that precise distance since y refers to the pumpkin's height.

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Answer:

D). the horizontal distance of the pumpkins from the launch site when their heights are the same

Step-by-step explanation:

I took the flipping test nickle

Answer:

2.5

Step-by-step explanation:

v = u + at is one of the kinematics equations.

Given v = 10, t = 2, u = 5, we will substitute these values into the equation to find a.

[tex]v = u + at\\10=5+2a\\2a=10-5\\2a = 5\\a = \frac{5}{2} \\= 2.5[/tex]

The height of package is 34 inches.

According to the statement

we have given that the perimeter of cylinderical package is 123 inches.

and we have to find the volume of this package.

So,

According to the perimeter

2(Pi)r + h = 123

and then

h = 123 - 2(Pi)r

then the volume become

V = (Pi) r^2h

V= (Pi) r^2 * [ 123 - 2(Pi)r ] = 123 (Pi) r^2  - 2(Pi)r^3

then differentiate it

dV/dr = 246(Pi) r - 6(Pi)r^2

Now take

r(246(Pi) - 6(Pi)r) = 0

then neglect r=0 and then find another value of r.

r = 246(Pi) / 6(pi)

here r=41 then

h = 123 - 2(Pi)r

h = 123 - 2(3.14)41

h = 123 - 2(Pi)r

Then put the value of r then h = 34 inches.

So, The height of package is 34 inches.

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Based on the calculations on this parallelogram, the correct equations are:

Based on the image of the parallelogram shown in the image attached below, we can logically deduce that the opposite sides of this parallelogram are all equal. Thus, we have:

Side DE = Side CF

6n - 1 = 5n + 9

6n - 5n = 9 + 1

n = 10.

From Side CF, we have:

CF = 5n + 9

CF = 5(10) + 9

CF = 59.

For the measure of side FE, we have

FE = 4n + 2

FE = 4(10) + 2

FE = 42.

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Complete Question:

Figure CDEF is a parallelogram.

Parallelogram C D E F is shown. The length of F C is 6 n minus 1, the length of C D is 4 n + 2, and the length of D E is 5 n + 9.

Which equations are correct? Select three options.

n = 10

n = 7

CF = 59

FE = 42

CD = 30

Answer:

A,C,D

Step-by-step explanation:

The measure that best describes the data is the median and the measure that might mislead the data is the mode

The mean is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{20* 2 + 50 * 3 + 60 * 6 + 70 * 3 + 80 * 4 + 90 * 4 + 100 * 2 + 130 * 1}{25}[/tex]

This gives

[tex]\bar x = \frac{1770}{25}[/tex]

[tex]\bar x = 70.8[/tex]

So, the mean is 70.8

The median is the middle number, and the position is calculated using

Median = (n + 1)/2 th

This gives

Median = (25 + 1)/2 th

Median = 13th

The 13th element is 70

So, the median is 70

The mode is the data element with the highest frequency.

So, the mode is 60

The line plot has outliers at 20 and 130.

This is so because 20 and 130 are far from other data values

When a dataset has an outlier, the best measure is the median

Hence, the measure that best describes the data is the median.

The measure that might mislead the data is the mode

This is so the highest occurring value does not necessarily represent the dataset

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A conditional probability of an event tells us that the event has already occured.

Given a _______ probability of an event is a ............. other event has already occurred.

We have to fill the blank with appropriate term or word associated with probability.

The right term is conditional.

Conditional probability of an event is a probability obtained with knowledge that some other event has already occured.

It is denoted as P(A I B).

It satisfies the following equation:

P(AIB)=P(A and B ) / P(B)

where P( A and B) is the probability of A and B together.

Hence conditional probability of an event is obtained with knowledge that some other event has already occured.

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Answer:

4:10

Step-by-step explanation:

4:10 = 4/10 = 2/5

12:20 = 12/20 = 6/10 = 3/5.

So 4:10 is smaller than 12:20 because 2/5 is less than 3/5.

Answer:

4:10

Step-by-step explanation:

First, I wrote each ratio as a fraction. Then I found a common denominator of 20. The fraction 4/10 is 8/20. Comparing numerators, 8 is less than 12, so the ratio 4:10 is smaller.

Answer:

y = (1/3)x + 7

Step-by-step explanation:

The general structure form of a line in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

The slope of a perpendicular line is the opposite-signed, reciprocal of the original line's slope. Therefore, if the slope of the original line is m = -3, the new slope is m = 1/3.

The y-intercept can be found by plugging the new slope and the values from the point (-3, 6) into the slope-intercept form equation.

m = 1/3

x = -3

y = 6

y = mx + b                                  <----- Slope-intercept form

6 = (-3)(1/3) + b                           <----- Insert values

6 = -1 + b                                    <----- Multiply -3 and 1/3

7 = b                                           <----- Add 1 to both sides

Now, that you have the slope and y-intercept, you can construct the equation of the perpendicular line.

y = (1/3)x + 7

Using the given information, the height of the tree is 48 ft

From the question, we are to determine the height of the tree

In the given diagram, the height of the tree is (x + 5) feet

First, we will determine the value of x

tan 47° = x / 40

x = 40 × tan47°

x = 42.89 ft

∴ The height of the tree = (42.89 + 5) ft

Height of the tree = 47.89 ft

Height of the tree ≈ 48 ft

Hence, the height of the tree is 48 ft.

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Answer:

No.  They cannon be on the same straight line.

Step-by-step explanation:

As explained in the attached graphic, the slopes are slightly different between the three points.

#1

h(2.5)

After 2.5s the ball was at 47ft

#2

g(0)

g(4)

g(7)

Range

#3

The distance between David's home and the airport is 210 miles.

let the distance traveled after first 1 hour = y

distance/speed = time

after 1 hour his speed = (35 + 15) = 50 mph

total time after 1 hour and 30 mins = 1.5 hr

y/50 + 1.5 = y/35

multiply through by350

7y + 525 = 10y

3y = 525

y = 525/3

y = 175 miles

In the first 1 hour, at 35 mph, distance covered = 35 miles

Distance from his home to airport = 175 miles + 35 miles = 210 miles

Thus, the distance between David's home and the airport is 210 miles.

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The width of his patio is 19.5 feet based on the information about the area given.

Area = Length × Width

175.5 = 19.5 × w

Width = 175.5/19.5

Width = 9 feet

The width of his patio is 19.5 feet.

The number of blocks that were used will be:

= 175.5/(1.5 × 1.5)

= 175.5/2.25

= 78 blocks

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Complete question

Gavin made the patio area out of square block that are 1.5 by 1.5 feet. The area of the patio is 175.5 ft² and the length is 19.5ft.

a. Determine the width of his patio.

b. Determine the number of blocks Gavin used to make his patio.

a) Substituting in n = 2,

[tex]\frac{3(2)^{2}}{2}=6[/tex]

b) Substituting in n = 5,

[tex]\frac{3(5)^{2}}{2}=\frac{75}{2}[/tex]

c) Setting the nth term to be greater than 50,

[tex]\frac{3n^{2}}{2}>50 \\ \\ n^{2} >\frac{100}{3} \\ \\ n>\frac{10}{\sqrt{3}} \\ \\ \lceil n \rceil = 6[/tex]