A nearby skating park charges $4 for skates and an hourly rate for each hour.
The sign on the right gives the prices for up to 3 hours of skating. Which linear
equation represents the given information where C is the total cost and h is the
number of hours spent in the park?

1 hour
2 hours
3 hours
$15
$30
$45

Using the Triangle Midsegment Theorem, the value of x in the figure is: 4.

The Triangle Midsegment Theorem states that:

The length of segment DE = 1/2(the length of segment BC)

Given the following;

DE = x + 1

BC = 4x - 6

Substitute

x + 1 = 1/2(4x - 6)

2(x + 1) = 4x - 6

2x + 2 = 4x - 6

2x + 2 - 4x = 4x - 6 - 4x

-2x + 2 = - 6

-2x + 2 - 2= - 6 - 2

-2x = -8

-2x/-2 = -8/-2

x = 4

Thus, using the Triangle Midsegment Theorem, the value of x in the figure is: 4.

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The garden will stretch by 2/3 miles.

Given that Garden covers an area of 1/6 of a square mile and the garde is 1/4 mile wide.

As we know, the garden is a rectangle shape.

Here, we will use the formula of area of rectangle.

Area of rectangle is equal to the product of length and breadth.

Area =l×b

Here, the give area=1/6 miles² and b=1/4 mile.

Now, we will substitute the values in the formula, we get

1/6=l×(1/4)

Further, we will multiply both sides with 4, we get

4/6=4l/4

4/6=l

Now, we will simplify the left hand side, we get

2/3=l

Hence, the length of garden stretch when garden covers an area of 1/6 of a square mile and 1/4 mile wide is 2/3 mile.

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The equation of parabola is [tex]y=1/4x^{2}+x/2-4\\\\[/tex].

A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape. A plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.

Given:

The equation of parabola in vertex form is

[tex]y=a(x-h)^{2} +k[/tex]

Being vertex here

h=-2

k=-5

According to given question we have

∴

Equation of parabola in vertex form is

[tex]y=a(x+2)^{2} -5[/tex]

. The parabola passes through point  (4,4)  So the point (4,4)  will satisfy the equation .

[tex]4=a(4+2)^{2} -5\\\\4=a*36-5\\\\9=a*36\\\\a=9/36\\\\a=1/4[/tex]

Hence the equation of parabola is

[tex]y=1/4(x+2)^{2} -5\\\\y=1/4(x^{2} +4+2x)-5\\\\y=1/4x^{2} +1+x/2-5\\\\y=1/4x^{2}+x/2-4\\\\[/tex]

Therefore, the equation of parabola is [tex]y=1/4x^{2}+x/2-4\\\\[/tex].

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the equation of parabola is missing

Answer:

4x[tex] \sf {}^{3} [/tex] +80x²+10x+2

Step-by-step explanation:

(x+20)4x²+10x+2

Let's simplify step-by-step.

(x+20)(4)x²+10x+2

Distribute:

=4x[tex] \sf {}^{3} [/tex] +80x²+10x+2

Answer:

5 x 4=20

Step-by-step explanation:

the x is a smaller number to tell you how many 5's there are which x=4 so the are 4 5's but you have to times(multiple) the two numbers.

5x4

=20

Answer:

1) 48

2)44

Step-by-step explanation:

Answer:  48 44 Are The Correct Answers

Step-by-step explanation:Hope This Helps

The weight loss program is not statistically significant because the results are likely to occur by chance. (Option D)

Now,

Hence, the given program is not statistically significant because the results are likely to occur by chance. (Option D)

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(COMPLETE QUESTION:

Determine whether the results below appear to have statistical​ significance, and also determine whether the results have practical significance.

In a study of a weight loss​ program, 7 subjects lost an average of 43 lbs. It is found that there is about a 22​% chance of getting such results with a diet that has no effect.

Does the weight loss program have statistical​ significance?

A.No, the program is not statistically significant because the results are unlikely to occur by chance.

B.Yes, the program is statistically significant because the results are unlikely to occur by chance.

C.Yes, the program is statistically significant because the results are likely to occur by chance.

D.No, the program is not statistically significant because the results are likely to occur by chance.)

The measure of the angle 2 is 122°.

Given that angles 1 and 2 form a linear pair,

angle 1 + angle 2 = 180 degrees         —— (1)

We've also been notified that angle 2 is 6 times the size of angle 1.

That is to say: angle 2 = (2×angle 1) + 6      ———- (2)

Putting the angle 2 value in (1) from (2)

180 = angle 1 + 2×angle 1 + 6

3×angle 1 = 174

1st angle = 58 degrees  ———-(3)

(1) and (3) come from:

angle 2 + 58 = 180

2nd angle = 122 degrees

As a result, angle 2 has a measure of 122 degrees.

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The amount each contestant will receive is as follows:

This year $52,000 college scholarship is being divided between the top two contestants .

Therefore,

Total amount to share to the top winners = 52000 dollars

The winner receives three times as much as the runner-up.

Therefore,

let

x = Amount received by the runner-up

Hence,

Amount the winner received = 3x

Therefore,

52,000 = 3x + x

52,000 = 4x

divide both sides by 4

4x / 4 = 52,000 / 4

x = 13000 dollars

Hence,

Amount the winner received =3(13000) = $39000

Amount received by the runner-up = $13,000

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Answer:

13

Step-by-step explanation:

The expression for modelling the pattern is n² + 2

Charlie can observe 38 guppy fish in month 6.

Given,

Number of guppy fish in Charlie's fish tank for the first time = 3

Number of guppy fish after one month = 6

Number of guppy fish in the following month = 11

The increasing pattern of guppy fish in the tank:

First month = 6 - 3 = 3

Second month = 11 - 6 = 5

So, we get that the number of guppy fish is increasing by odd numbers.

That is, 3, 6, 11, ........

Now, we have to find an expression for this pattern.

First term is 3.

That is, first term² + 2 = 1² + 2 = 3

Let n be the number of term.

n = 3

So, third term be:

3² + 2 = 9 + 2 = 11

So the expression for modelling the pattern is n² + 2

Now, we have to find the number of guppy fish in month 6.

That is,

n = 6

So,

n² + 2

6² + 2 = 36 + 2 = 38

That is, Charlie can observe 38 guppy fish in month 6.

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The statement  that "If two adjacent angles form a right angle, then the angles are complementary", is true

The conditional is given as:

If two adjacent angles form a right angle, then the angles are complementary

As a general rule, complementary angles add up to 90 degrees i.e. right angle

This means that adjacent angles that add up to 90 degrees are complementary angles

Hence, the statement  that "If two adjacent angles form a right angle, then the angles are complementary", is true

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According to the calculations made by Bob after downloading and calculating the correlation value as 0.5 from a given data set, he concludes that as the number of bedrooms in a particular home increase there is an increase in the selling price of the bed.

This increase in the selling price due to the increase in the number of bedrooms can be explained with the help of the Law of Demand which states that as the demand for a certain product increases its cost or the selling price also increases.

Thus, when Bob calculates the correlation factor, he finds that as the number of bedrooms increases there is also a hike in the selling price. As there should be a surplus to fulfill the demand for bedrooms.

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Answer:

slope = - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (2, - 1)

m = [tex]\frac{-1-1}{2-(-2)}[/tex] = [tex]\frac{-2}{2+2}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]

According to the question, the standard equation for the circle is [tex]x^{2} +y^{2} =r^{2}[/tex] in which the points (x, y) are the circumference point and 'r' is the radius of the circle.

The given expression for the circle is shown below:

[tex]x^{2} +y^{2} -12x+6y-19=0[/tex]

Bring same variable terms to one side and again re-write the expression:

[tex]x^{2} -12x+y^{2} +6y-19=0[/tex]

Now, to do factors of the given expression add and subtract 36,9 on both the sides

[tex]x^{2} -12x+36+y^{2} +6y+9=19+36+9[/tex]

Factors can be re-written as:

[tex](x-6)^{2} +(y+3)^{2}=64[/tex]

Comparing the calculated equation for the circle with the standard equation, we circle

The center points as (6,-3) and radius as (r = 8).

Hence, the correct answer is Center(6,-3), r = 8.

What is circle?

The circle can be defined as a symmetrical shaped. It has more than one points and all are at the equidistant from the center.

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Answer:

B

Center (7, –5); r = 8

Step-by-step explanation:

Answer: 1

Step-by-step explanation:

4^(-1) / 4^(-1)=

1/4 / 1/4=

1/4 * 4/1=      ==> Dividing by a number is basically multiplying its reciprocal

1*4/(4*1)=

4/4=1

The solution of the system of linear equations behind the geometric system is (x, z) = (29, 13). The measures of the angles RIG and ZIM are 59° and 140°, respectively.

In this problem we find a geometric system generated by lines GZ, AM and IR, in which two variables are shown (x, z) and whose values can be found by applying the concepts of complementary and supplementary angles.

A group of angles are complementary if the sum of their measures equals 90°, and supplementary if that sum equals 180°. This system can be represented by the following system of linear equations:

(3 · x - 56) + 90 + (4 · z + 7) = 180       (1)

(4 · z + 7) + (x + 2) = 90                        (2)

By (1):

(3 · x - 56) + (4 · z + 7) = 90

3 · x + 4 · z - 49 = 90

3 · x + 4 · z = 139                                  (1b)

By (2):

x + 4 · z = 81                                         (2b)

The solution of the system of linear equations behind the geometric system is (x, z) = (29, 13).

Then, the measures of the angles RIG and ZIM are, respectively:

m ∠ RIG = 4 · z + 7

m ∠ RIG = 4 · 13 + 7

m ∠ RIG = 59°

m ∠ ZIM = 360° - (3 · x - 56) - 90° - (4 · z + 7) + (x + 2)

m ∠ ZIM = 360 - 3 · 29 - 56 - 90 - 4 · 13 + 7 + 29 + 2

m ∠ ZIM = 140°

The measures of the angles RIG and ZIM are 59° and 140°, respectively.

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180g = 0.180 kg or there are 0.180 kilograms in 180 grams.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.

A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.

The sentence states an equality between a units of weight in grams (g) and kilograms (kg).

From there, we can say that we are asked how many kilograms are there in 180 grams.

Converting grams to kilograms, we must use the conversion

1 g = 0.001 kg

180g = 180 (0.001) kg

180g = 0.180 kg

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The expression is 14 - 14.

Subtraction is a mathematical operation that is used to determine the difference between two or more numbers. The sign used to depict subtraction is -. Other mathematical operations are addition, multiplication and division.

In order to determine the expression for the amount of gas left, we need to subtract the gas bought from the gas used: 14 - 14

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Answer:

$6.08

Step-by-step explanation:

16 ounces = 1 pound

4 pounds 12 ounces = 4 12/16 pounds OR 4 ¾ pounds

4¾ ≈ 4.75

4.75 pounds x $1.28 = $6.08

Answer:

Negative 2.5 greater-than negative 1.5

C

Step-by-step explanation:

-2.5 < -2

Answer:

The expression or number to which the logarithm is operated on is called the argument. From the mathematical expression (x=logbn) ( x = l o g b n ) , n is the argument of the logarithm. The argument of a log function is always positive and should not be equal to 1. Hope this answer helps you.

Answer:

She will pay her mom back and have 20 dollars over if she works one hour.

Step-by-step explanation:

Answer:

4​(​7) is​ 7 units from​ 4, in the​ forward direction.

Step-by-step explanation:

The arithmetic and geometric average returns for a stock with annual returns of 9.4 percent, 8.2 percent, -7.3 percent, 4.1 percent, and 9.5 percent are 4.78% and 4.58% respectively.

The shares of ownership in a corporation or company that make up stock (also known as capital stock) in the financial world. A single share of stock represents a fractional ownership in the firm in relation to the entire number of shares (especially in American English, where the word "stocks" is also used to refer to shares). This typically entitles the shareholder (stockholder) to that portion of the company's earnings, proceeds from the sale of assets (after paying off all senior claims such as secured and unsecured debt), or voting rights, often allocating these in proportion to the amount of money each stockholder has invested.

Calculations:

Arithmetic returns=Total returns/Total time period

=(9.4+8.2-7.3+4.1+9.5)/5=4.78%

Geometric returns=[(1+rate1)(1+rate2)........(1+rate5)]^(1/5)

=[(1+0.094)(1+0.082)(1-0.073)(1+0.041)(1+0.095)]^(1/5)

=4.58%

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Adding integers with a common sign.

When adding two integers with a common sign, we just add the absolute value of the numbers and the resulting answer is marked with the same sign given in the question.

This question has two possible answers.

Possibility 1:

Both the integers are of positive sign. As a result, the resulting integer after addition is positive.

Example:

Let c = 45 and d = 53.

The sum of c and d is then

sum = c + d = 45 + 53 = 98

Possibility 2:

Both the integers are of negative sign. As a result, the resulting integer after addition is negative.

Example:

Assume c = -23 and d = -61.

The sum of c and d is then

sum = c + d = (-23) + (-61) = -(23 + 61) = -84

Hence, we have added integers with a common sign.

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Answer:

The diver is at a depth of [tex]-5\frac{1}{15}[/tex].

_____________________________________
What we have given:

Initial dive: [tex]1\frac{2}{3}[/tex] = [tex]x[/tex]
Additional dive: [tex]3\frac{2}{5}\\[/tex] = [tex]z[/tex]

Given the context, we can assume that sea level is 0ft.

So we have:
[tex]d=0-1\frac{2}{3}-3\frac{2}{5}[/tex] (d = depth)|

[tex]d=0-\frac{5}{3}-\frac{17}{5}[/tex] <- Convert mixed numbers to improper fractions.
[tex]d=-\frac{5}{3}-\frac{17}{5}[/tex] <- Simplify.
[tex]d=-\frac{25}{15}-\frac{51}{15}[/tex] <- The LCM between 3 and 5 is 15, so adjust the fractions accordingly.

(NOTE: Remember everything you do to the denominator must be replicated on the numerator as well!)

[tex]d=\frac{-25-51}{15}[/tex] <- Since the denominators are equal, combine the fractions.
[tex]d=\frac{-76}{15}[/tex]
[tex]d=-\frac{76}{15}[/tex] <- Apply the following fraction rule = [tex]\frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]d=-5\frac{1}{15}[/tex] <- Convert the improper fraction to a mixed number and there is your final answer.

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Answer: E: Infinitely many solutions

Step-by-step explanation:

Starting with 5x - 7x + 6, let's combine like terms.

5x - 7x is -2x.

Thus, we have -2x + 6 = -2(x-3)

Using the distributive property for the right side, we multiply -2 * x, and get -2x, and -2 * -3 and get +6.

Now we have -2x + 6 = -2x + 6. We have the same equation here, and know that there is infinitely many solutions here off the bat.

For sake of computations, let's solve and show our work.

Subtracting 6 from both sides, we have -2x = -2x.

Adding 2x to both sides, we get 0 = 0.

Thus, we have infinitely many solutions.

Answer:

0.375

Step-by-step explanation:

see above