The height of a statue of a boy was 12 meters and the scale used was 4 meters: 1 foot. Find his actual height.

Solving proportional relationship and options given we have value of x in second row as 5 and in third row as 8, value of y in third row as 2.4

What is proportional constant ?

The ratio between two proportional quantities' constant values is known as the constant of proportionality.

When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship.

The Direct Variation and Inverse Variation types of proportions between the two provided quantities determine the proportionality constant's value.

To show proportional relationship we need to have  [tex]\frac{y}{x}[/tex] as a constant value k.

From first set of data, we can have our constant k as

[tex]k=\frac{.6}{2} =0.3[/tex]

Now to fill 2nd row of table we have value of y given and as discussed above  [tex]\frac{y}{x}[/tex]  will remain constant. So, solving we get

 [tex]x = \frac{1.5}{0.3} = 5[/tex]

So, value of x in second row will be 5

For third row we can substitute as value of x as 8 and value of y as 2.4 that will give us proportional constant as calculate in above cases.

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Answer:

$4,140.00

Step-by-step explanation:

Interest = principle x rate x time

I = 3600 x .03 x 5

I = 540

Add the interest to what is already in the account

540 + 3600

4140

Step-by-step explanation:

based on the geometric mean theorem

h² = pq

h = height of the main right-angled triangle.

p and q are the segments of the baseline of the main right-angled triangle.

12² = 36x

144 = 36x

x = 144/36 = 4

so, DC is 4 units long.

the height of 4.6 units when the trapezoid's area is 70 units and its first and second bases are

Area is a mathematical concept that expresses the size of a region on a planar or curved surface. A shape's "space enclosed within the perimeter or the boundary" is referred to as its area. Math formulas are used to determine the area of various forms.

given

area of the trapezoid is 70 units

and the 1st base = 20 units and 2nd base = 10 units

length CE ?

area of trapezoid = 1/2( b1 + b2)*h

70= 1/2 (20 + 10 )*h

70 = 1/2(30)*h

h = 4.6 units

the height of 4.6 units when the trapezoid's area is 70 units and its first and second bases are

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Answer: False

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

(-4)2 | -7 - (-5)| -23

-4*2=-8

-7- -5=-2

|-2|=2

-8*2=16

16-23=-7

If there is a problem with this answer please feel free to tell me, thanks :)

The table for the function y = 5^x should be completed as follows;

x           y

-1          0.2

0           1

1            5

2           25

A graph of the given function y = 5^x with the points (0, 1) and (1, 5) is shown in the image attached below.

In Mathematics, an ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

Next, we would determine the ordered pairs that would complete the table for the function y = 5^x as follows;

When x = -1, the value of y is given by;

y = 5^-1

y = 0.2 or 1/5.

When x = 0, the value of y is given by;

y = 5^0

y = 1

When x = 1, the value of y is given by;

y = 5^1

y = 5

When x = 2, the value of y is given by;

y = 5^2

y = 25

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Answer:

D) [tex]x^2+8x+16=(x+4)^2[/tex]

Step-by-step explanation:

[tex]x^2+8x+(8/2)^2=x^2+8x+16=(x+4)^2[/tex]

Answer:

= about 1436.75504

Step-by-step explanation:

V = 4/3 π r³

Step-by-step explanation:

since it's -14 then it will be√-14

√-14=√-2 multiplied is by √7

so that will be √-2√7

The correctly labels the population of employees is, 001 - 250.

What is population?

The term "population" refers to all citizens who are either permanently residing in a nation or are only temporarily absent from it. This indicator displays the population of a given area on a regular basis. Growth rates are the yearly changes in population brought on by births, deaths, and net migration.

Given:

The CEO of a company wants to determine if taking the employees to a company retreat would boost their morale.

He decides to use a random number table to survey a simple random sample of 50 of the 250 employees.

As the population consist of 250 employees and simple random sample of size 50, to use a random number table to survey a sample random sample of 50 of the 250 employees, the population of employees should be labeled as 001-250.

Hence, the correctly labels the population of employees is, 001 - 250.

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The speed (in km/hr) of the ships changing at 4.00pm is 20.62km/hr

The given parameters are;

The distance between A and B = 170km=m

The distance between B and C is 30km=m

Time is 12.00 noon to 4.00 pm = 4 hours

From the given parameters,

m=170-35*4 = 170-140=30

The Distance (D)=√(30²+120²

D=30*√(1²+4²)

Simplifying to get

30√17

From the Pythagoras theorem,

D²=m²+n²

Applying differential calculus,

⇒2m(dm/dt)+2n(dn/dt)=2D(dD/dt)

Applying the figures from the question we have

2*30*(-35)+2*120*30=2*30√17*dD/dt

Simplify to get

120-35=√17dD/dt

This implies that dD/dt=85/√17

⇒5√17=20.6155281km/h

Therefore, the speed between the ships is ≅20.62km/hr

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The thing that the horizontal line signifies in the confidence interval plot is D. These horizontal lines are placed to help you visually locate the dot.

A confidence interval is a range of values that contains the value of an unknown population parameter. Given the characteristics of your sample data, these intervals represent a plausible domain for the parameter.

Confidence intervals are calculated using a specified confidence level and are derived from sample statistics. Confidence intervals are used by statisticians to quantify uncertainty in a sample variable. These horizontal lines are placed to assist you in visualizing the dot.

In conclusion, the correct option is D.

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Answer:

Below

Step-by-step explanation:

a)  All possible rolls  ( 36 of them)

1   1 , 2 , 3 , 4 , 5 , 6

2   1, 2, 3, 4, 5 , 6

3    1 , 2 , 3 , 4,5,6

4  1,2,3,4,5,6

5  1,2,3,4,5,6

6  1,2,3,4,5,6

b) underlined above    21 out of 36    or 7/12

c )   3 out of 36    1/12

d )  11/36

Answer:

x ≈ 10.6

y = 15

Step-by-step explanation:

The opposite angles in an inscribed quadrilateral are supplementary.

Therefore:

(4y+14) + (7y+1) = 180

=> 11y + 15 = 180

=> 11y = 165

=> y = 15

7x+1 + 105 = 180

=> 7x + 106 = 180

=> 7x = 74

=> x ≈ 10.6

Answer:

-2.5

Step-by-step explanation:

For a quadratic equation [tex]ax^2 + bx+c=0[/tex], the sum of the roots is [tex]-b/a[/tex].

Here, [tex]b=5[/tex] and [tex]a=2[/tex], so the sum is [tex]-2.5[/tex].

The length of the congruent triangles are as follows:

BC = 36

EF = 36

Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

ΔABC≅ΔDEF

Let's find the length of the given sides as follows:

BC = x + 20

EF = 2x + 4

Therefore,

BC = EF

x + 20 = 2x + 4

x - 2x = 4 - 20

- x = -16

x = 16

Therefore,

BC = x+20 = 16 + 20 = 36

EF = 2x+4 = 2(16) + 4 = 32 + 4 = 36

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Applying the properties of a rhombus, the value of each angle listed are:

m∠JKL = 72°

m∠MLK = 108°

m∠JMK = 36°

m∠MJL = 54°

m∠KNL = 90°

A rhombus is a quadrilateral with the following properties:

Given, m∠JKM = 36°, apply the properties of a rhombus to solve the missing values.

m∠JKL = 2(36)

m∠JKL = 72°

m∠MLK = 180 - 72 [adjacent angles are supplementary in a rhombus]

m∠MLK = 108°

m∠JMK = 36°

m∠MJL = 1/2(m∠MLK)

m∠MJL = 1/2(108)

m∠MJL = 54°

m∠KNL = 90° [bisection of the diagonals of a rhombus at right angles).

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Answer:

4.67 (nearest hundredth)

Step-by-step explanation:

In 3 weeks, Landscape Elementary uses 14 reams of paper.

In 1 week, Landscape Elementary uses 14/3 reams of paper. = 4.66666...

The digit at thousandth place is 6 and it is more than 5. Thus add 1 with hundredth digit.

4.66666... = 4.67 (nearest hundredth)

The total years taken to double the money according to Compounding will be 13.75 years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 2%

amount = $1700

Total amount = $2200

Compounded monthly,

so formula becomes,

Total amount = amount (1+r/400)^4t

T = A[tex](1+r/400)^{4t[/tex]

2200 = 1700(1 +2/400)^4t

22/17 = (1 +1/200)^4t

22/17 = (1.005)^4t

1.29 = (1.005)^4t

taking log on both sides

0.11/0.002 = 4t

t = 13.75 years.

Hence the time taken to double the money is 13.75 years.

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The equation of a line into slope is 1/2x+1

A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.

Y equals mx plus b is actually the slope intercept form. Because it provides both a slope and an intercept, the form is known as a slope intercept form.

A line's slope and y-intercept are expressed in the following formula: y=mx+b. The y-intercept, which is usually represented in coordinate form as (0,b), is the point where the line crosses the y-axis.

y=1/2x+1

8y-4x=8

Add 4x to both sides.

8y=4x+8

Divide 8 (the one with y) by both sides.

y=1/2x+1

Therefore the equation of a line into slope is 1/2x+1

The complete question is : 8y−4x=8 Put the following equation of a line into slope-intercept form, simplifying all fractions.

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12 bottles of soda cost  $15.84  next week

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

Price of  5 bottles = $6

Price of  1 bottle = 6/5 = $1.2

10% of 1.2 = (10/100)*1.2 = 0.12

new price of 1 bottle = 1.2+ 0.12 = $1.32

Price of  12 bottles = 12*1.32 = $15.84

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An inequality that can be used to determine how much material, x, Paul should buy is x ≥ 196.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other.

Given:

Paul is making picture frames.

He wants to make at least 8 picture frames and needs 24.5 inches of material for each frame.

To find the total material for 8 frames:

Multiply by 8 to material for one form

24.5 x 8

= 196 inches

To write an inequality that can be used to determine how much material, x, Paul should buy:

x ≥ 196 inches.

To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more.

You must flip the inequality sign if you multiply or divide either side by a negative number.

Therefore, the inequality is x ≥ 196.

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The dimensions of the rectangular garden to maximize the area is length = width = 75 meters.

Let l be the length and w be the width of the rectangular garden.

We need to find the dimensions of the rectangular garden of greatest area that can be fenced off (all four sides) with 300 meters of fencing.

The perimeter of the  rectangular garden = 300 meters

We know that the perimeter of the rectangle =2(length + width)

300 = 2(l + w)

l + w = 150               .......(1)

Now, the maximum area of a  rectangular garden is when Length  = width

So, for equation 1

l + l = 150

l = 75 meters

So, w = 75 meters

And the area of the rectangular garden = length * width

                                                               = 75 * 75

                                                               = 5625 m²

So the maximum area of the  rectangular garden is 5625 m²

Therefore, the dimensions of the garden to maximize the area is length = width = 75 meters and maximum area is  5625 m²

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Answer:

the average contribution to the political campaign was $0.12.

Step-by-step explanation:

To find the average contribution to the political campaign, we first need to convert the total amount of money contributed and the number of people who contributed to scientific notation.

The total amount of money contributed to the political campaign was $9.48 million, which can be written in scientific notation as $9.48 * 10^6.

The number of people who contributed to the campaign was 79 thousand, which can be written in scientific notation as 79 * 10^3.

To find the average contribution, we need to divide the total amount of money contributed by the number of people who contributed. Therefore, we can substitute the values in scientific notation into the formula to find the average contribution:

Average contribution = Total amount / Number of people

                   = 9.48 * 10^6 / 79 * 10^3

                   = 9.48 / 79

                   = 0.12

Therefore, the average contribution to the political campaign was $0.12.

a) The Test statistic of the hypothesis is; 0.23

b) The p-value from the test statistic is; 0.409

c) The final conclusion is there is not sufficient evidence to determine whether the antidepressant drug had an effect on changing working habits after one year.

Test statistic is defined as a number, calculated from a statistical test, used to find if your data could have occurred under the null hypothesis. In this case, we are dealing with proportions and as such the test statistic has the formula;

z = (p1 - p2)/standard error

p1 = 14/167 = 0.084; s1 = √(0.084 * 0.916/167) = 1.285

p2 = 316/833 = 0.38; s2 = √(0.38 * 0.62/833) = 0.0168

Hence, for the distribution of differences, the mean and the standard error are given as follows:

Mean: p = 0.38 - 0.084 = 0.296

Standard error: s = √(1.285² + 0.0168²) = 1.2854

a) Test statistic = p/s = 0.296/1.2854

Test statistic = 0.23

b) From p-value from z-score calculator, we get that;

p-value = 0.409

c) The p-value is greater than the significance value of 0.04, we fail to reject the null hypothesis and conclude that there is not sufficient evidence to determine whether the antidepressant drug had an effect on changing working habits after one year.

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Answer: 20/48

(simplified) 5/12

Step-by-step explanation:

We will use 6/8 - 2/6 for our example

6/8 - 2/6

Multiply the denominator on the right side by the denominator on the left side: 6x8 = 48

Make 48 the denominators on both sides: /48,  /48

Now multiply the denominator on the left side with the numerator on the  left side: 6x6 = 36

Make the first fraction's numerator 36: 36/48

Now multiply the denominator on the left side by the numerator on the right side: 8x2 = 16

Now make 16 the numerator of the second fraction: 16/48

Now that the denominators are the same, we can subtract!

36/48-16/48 = 20/48

Now to simplify:

divide 20/48 by 4 = 5/12

So the answer is 20/48 and when it is simplified it comes out to 5/12

This is how you subtract fractions with different denominators.

You can use the same method when adding, the only difference is that instead of adding in the last step, you add instead!

Answer:

4 and 1/2

Step-by-step explanation:

left side must be ewual to right side. after you substract 12x-4x you get 8x+2 on right side. you than find a number on the left side, whit which you have to multiply 2x to get 8x(same number as on the other side) and you get 4. lastly you have to find a number that gives you 2 when multiplied with 4 and it is 1/2

7.14 unit² is the area of the rectangle shown on the coordinate plane

The length and breadth of the rectangle multiplied together provide the area of the rectangle. To determine the area occupied by a rectangle within its perimeter, we compute the area of the rectangle.

Consider rectangle with vertices A(-1,-2), B(-3,-4), C(-6,-1) and D(-4,1). The area of the rectangle is:

Area = length × width

Now, find the length and the width:

Length (BC) = [tex]\sqrt{[-3-(-6)]^2 + [(-4)-(-1)]^2}[/tex]

or, BC = [tex]\sqrt{(3)^2 +(-3)^2}[/tex]

or, BC = [tex]\sqrt{18}[/tex] unit

Width (AB) = [tex]\sqrt{[(-1) -(-3)]^2 + [(-2)-(-4)]^2}[/tex]

or, AB = [tex]\sqrt{(2)^2 +(2)^2}[/tex]

or, AB = [tex]\sqrt{8}[/tex] unit

Then the area of the rectangle ABCD is

Area(ABCD) = length (BC) × width (AB)

or, Area(ABCD) = [tex]\sqrt{18} *\sqrt{8}[/tex]

or, Area(ABCD) = 7.14 unit²

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