< The concession stand at the baseball park sells food in value packs. The ratio in the value pack is 4 hot dogs 2 drinks: 1 bag of chips. A tape diagram representing the ratio of each item is shown. hot dogs drinks chips a. Describe what each small rectangle in the tape diagram represents b. What is the least total amount of items in a value pack? c. How many bags of chips are in a value pack if there are 10 drinks? ​

x=12in

Slope of ramp= SecФ =5/3

Let the height of first point be H1

Let the height of second point be H2

Then, H1=27in (Provided in the question)

         H2=12in (Provided in the question)

The base of the right angled triangle then = H1-H2

Let the perpendicular be denoted as p

Let the base be denoted as b

Let the hypotenuse be denoted as h

then, b=H1-H2

b=27-12

b=15

The Formula of SecФ=1/CosФ

Since, CosФ= Base/Hypotenuse

SecФ=/Hypotenuse/Base

SecФ= h/b

SecФ= 5/3 (Provided in the question)

then,

5/3=15/b

cross multiplying

5b=15x3

b=15x3/5

cancelling out 15 by 5

b=3x3

b=9

From Pythagoras theorem

[tex]h^{2}[/tex]=[tex]p^{2}[/tex]+ [tex]b^{2}[/tex]

putting values in the equation above:

[tex]15^{2}[/tex]=[tex]p^{2}[/tex] +[tex]9^{2}[/tex]

15x15=[tex]p^{2}[/tex]+81

225-81=[tex]p^{2}[/tex]

[tex]\sqrt{225-81}[/tex]=p

[tex]\sqrt{144}[/tex]=p

12=p

Since slope of ramp is equivalent to angle of depression

thus, p=x

x=12in

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If the equation 2(x-7) = 36, then the value of x is 13 and 1

The equation is

[tex](x-7)^2[/tex] = 36

The equation is defined as the statement the connect the two expression with an equal sign.

We know the square of 6 is 36

[tex]6^2[/tex] = 36

Substitute the value in the equation

[tex](x-7)^2=6^2[/tex]

Apply square root in the both side of the equation

[tex]\sqrt{(x-7)^2} = \sqrt{6^2}[/tex]

Then the equation will become

x - 7 = ± 6

If the value is +6

x - 7 = 6

Add both side of the equation by 7

x - 7 +7 = 6+7

x = 13

If the value is -6

x - 7 = -6

Add both side of the equation by 7

x - 7 + 7 = -6 + 7

x = 1

Hence, If the equation 2(x-7) = 36, then the value of x is 13 and 1

The complete question is:

Given [tex](x-7)^2=36[/tex], find the value of x.

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The difference between an independent sample and a dependent sample is that the dependent sample for one set of items is paired measurement while measurements made on two samples are termed an independent sample.

In statistics, while considering two samples and conducting a hypothesis test, one should be aware of which type of test should be conducted based on samples whether they are dependent or independent. If the value of another sample is affected by any one sample then the samples are dependent. If no information can be deduced from the other sample using one sample then the samples are independent.

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The corresponding estimate for numbers in 1,2,3 and 4 are 10, 24, 21 and 153

Estimation and approximation is the process of using rounded values when presenting numerical data and making rough calculations.

The digits 1,2,3 and are rounded down and digits 5,6,7,8 and 9 are rounded up

1.  2.1 x 5.12 =  2 x 5 = 10

Explanation: The number after the digit 2 in 2.1 is 1, we will round down 2.1 to 2. Also, the number after the digit 5 in 5.12 is 1, we will round down 5.12 to 5

2. 12.3 x 1.6 = 12 x 2 = 24

Explanation: The number after the digit 12 in 12.3 is 3, we will round down 12.3 to 12. Also, the number after the digit 1 in 1.6 is 6, we will round up 1.6 to 2

3. 6.5 x 3.1 = 7 x 3 = 21

Explanation: The number after the digit 6 in 6.5 is 5, we will round up 6.5 to 7. Also, the number after the digit 3 in 3.1 is 1, we will round down 3.1 to 3

4. 51.3 x 2.7 = 51 x 3 = 153

Explanation: The number after the digit 51 in 51.3 is 3, we will round down 51.3 to 51. Also, the number after the digit 2 in 2.7 is 7, we will round up 2.7 to 3

Therefore, the estimate for 1,2,3 and 4 are 10, 24, 21 and 153 respectively

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The correct option ; Quadrilateral, has the given information describing quadrilateral UVWX.

For the given values in the question;

In the quadrilateral UVWX

As, none of the sides are equal to other and none of the angles are equal to the other.

Thus, the this information shows the values are given for quadrilateral.

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Answer:

Your first option is correct but your second is wrong

Step-by-step explanation:

In option b-

when an employee receives 10% additional for each of the following weeks:

10% of 200=  10/100 x200= 20

it means he will get $20 in extra in every week

so it will be- 220,240,260

Ella answer makes sense because the value of  ? is 4

Given: the equation 32 divided ? =8 she says the value of ? is 4

32 / ? = 8    

Let x represent ? in the equation, thus:

32 / x = 8         cross multiply

8x = 32

x = 32/8

x = 4

Since x = 4. This implies ? = 4

Also, the value that divides 32 to give is 4

Since the value of ? is 4. Therefore, Ella's answer makes sense

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By applying the lowest common multiple approach, Kyra may have acquired up to 12 rocks.

What does common factor mean?

A common factor is a whole number that is a factor of at least two other numbers. The highest common factor is the largest factor that will divide into two or more numbers (HCF). The phrase "lowest common multiple" refers to the smallest multiple that two or more numbers have in common (LCM).

The least common multiple of 2, 3, and 4 can be used to determine how much rock Kyra has.

Several of:

2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

3 = 3, 6, 9, 12, 15, 18, 21

4 = 4, 8, 12, 16, 20

The smallest number that 2, 3, and 4 have in common is 12. There are therefore 12 rock piles in Kyra's possession.

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Answer:

Side BC is congruent to side YZ

The capital invested by q is $60,000 when p invested capital of $40,000.

According to the question,

We have the following information:

The ratio of the profits earned by by p and q is 2:3.

Amount invested by p = $40,000

Now, let's take the amount invested by p to be $2x and the amount invested by q to be $3x.

So, we have the following expression:

2x = 40000

x = 40000/2

x = $20000

Now, putting the value of x in 3x in order to find the amount invested by q:

3*20,000

$60,000

Hence, the amount invested by q is $60,000 when p invested capital of $40,000.

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The dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .

Let length be l and width be b of garden .

According to question ,

l + 2b = 1040

Area of garden = l * b

Substituting value of l in formula for area ,

Area = ( 1040 - 2b ) * b = 1040b - 2[tex]b^{2}[/tex]

Taking derivative of Area wrt. b and putting it equal to 0 ,

1040 - 4b = 0

b = 1040 / 4

b = 260 feet

Therefore , l = 1040 - 520 = 520 feet .

Maximum Area = 260 * 520 = 135200 [tex]feet^{2}[/tex] .

Hence , the dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .

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Answer:

Step-by-step explanation:

     I am going to transform this equation into slope-intercept form, as it is usually easier to graph it that way.

  Given:

-8 + x = 4y - 16

  Add 16 to both sides of the equation:

-8 + x + 16 = 4y

  Divide both sides of the equation by 4:

-2 + [tex]\frac{1}{4}[/tex]x + 4 = y

  Reflexive property and combine like terms:

y = [tex]\frac{1}{4}[/tex]x + 2

  Now, we will graph. The 2 is our y-intercept and the  [tex]\frac{1}{4}[/tex] is our slope, graphed as "rise over run." This means we will rise one unit up and run four units right.

      See attached.

Darryl receive $579.44  in dividends every year .

In the question ,
it is given that

Darryl's portfolio

number of shares of Essentia Inc. = 66

dividend received from each share in a year = $1.79 per share

So , amount of dividend received from Essentia Inc. = 66 × 1.79

= $118.14

number of shares of SFT Legal = 95

dividend received from each share in a year = $2.62 per share

So , amount of dividend received from SFT Legal = 95 × 2.62

= $248.9

number of shares of Grath Oil = 180

dividend received from each share in a year = $1.18 per share

So , amount of dividend received from Essentia Inc. = 180 × 1.18

= $212.4

So , total dividend Darryl receives = $118.14 + $248.9 + $212.4

= $579.44

Therefore , amount of dividend received by Darryl each year is $579.44  .

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The measure of width of given figure is 2 units. Therefore, option B is the correct answer.

From the given figure, the length is 9 units and the width is 1 unit.

Length is defined as the measurement or extent of something from end to end. In other words, it is the larger of the two or the highest of three dimensions of geometrical shapes or objects. For example, a rectangle has its dimensions as length and breadth.

From the figure, the width is 1+1=2 units

The measure of width of given figure is 2 units. Therefore, option B is the correct answer.

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The estimate of the population proportion of defectives is 0.05.

Given that,

There are 10 different samples of 50 observations, that is, total of 500 observations.

To find : The estimate of the population proportion of defectives

And total number of defectives from 500 observations is (5+1+1+2+3+3+1+4+2+3) = 25

Thus, the point estimate for the population proportion defectives will be,

=25/500=0.05

or just obtain the individual proportion of each sample and then take their average to obtain the same result.

Thus, the point estimate for the population proportion defectives will be 0.05

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The shortest total length of fence this can be done with will be 440 m as the total area is 2000 m².

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. The distance around an object is called the perimeter. For instance, the yard of your home is fenced in. The fence's length serves as the perimeter. Your fence is 200 feet long if the yard is 50 feet by 50 feet.

Here,

The area=2000 m²

xy=2000

x=2000/y

p=4x+2y

p=4*(2000/y)+2y

=8000/y+2y

p'=-8000/y²+2

-8000/y²+2=0

2y²-8000=0

y²-4000=

y²=4000

y= 20 m

p=8000/20+2*20

p=400+40=440 m

Given that the total area is 2000 m², the shortest total length of fence that can be used is 440 m.

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The largest area that can be enclose in straight wall is 2450 m².

Let 'x' be the length of rectangle.

Let 'y' be the width rectangle.

Perimeter =  140 meters

2x + y = 140      

y = 140 - 2x

Area = xy

Put the value of y in area.

Area = x(-2x + 140)

Area = -2x² + 140x

Differentiating the area with respect to x.

dA/dx = -4x + 140

Put dA/dx = 0 to get the critical point.

-4x + 140 = 0

x = 140/4

x = 35

Largest area at x = 35.

y = 140 - 2x

y = 140 - 2×35

y = 70

Area = xy

Area = 70×35

Area = 2450 m²

Thus, the largest area that can be enclose in straight wall is 2450 m².

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Using the compound amount formula, the amount after 40 years is 2000(107/100)^40.

In the given question,

Esther got a summer job and decided to set aside $2000 to prepare for retirement without making monthly contribution.

She invests in the US stock market through as index fund that averages a 7% return compounded annually over this 40 year period.

We have to find the total balance in the account after 40 years.

We have to find total balance compounded annually.

The formula of the compound amount is

A = P(1+r/100)^n

where A = Amount

P = Principal Amount

r = interest rate

n = time

From the question we know that

P = $2000, r = 7%, n = 40

Now putting the value in formula

A = 2000(1+7/100)^40

Simplifying

A = 2000(1×100/100+7/100)^40

A = 2000(100/100+7/100)^40

A = 2000((100+7)/100)^40

A = 2000(107/100)^40

You can find the amount after simplifying the amount.

Hence, the amount after 40 years is 2000(107/100)^40.

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The inequality that represents the the possible numbers of x pairs of socks you can buy when you buy 2 pairs of sneakers, using a system of equations, is of:

y ≤ 7.

A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of the problem from which the system was built.

For this problem, the variables are given as follows:

You have a $250 card to use at a sporting goods store. Each pair of sneakers is worth $80 and a pair of socks costs $12, hence the inequality regarding the total spending is:

80x + 12y ≤ 250.

When two pairs of sneakers are bought, we have that:

x = 2.

Hence the inequality regarding how many pairs of socks can be bought is:

80(2) + 12y ≤ 250.

160 + 12y ≤ 250.

12y ≤ 90

y ≤ 90/12

y ≤ 7. (rounded down, as you can buy 7 pairs of socks but not 8).

The cost of a pair of socks is of $12.

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The coordinates of the vertices after a rotation 270° counterclockwise around the origin is

T' = (-8, -4)

U' = (-8, -6)

V' = (-3, -9)

W' = (-3, -7)

The coordinates of T = (4, -8)

The coordinates of U = (6, -8)

The coordinates of V = (9, -3)

The coordinates of W = (7, -3)

The rule of rotating 270 degree clockwise around the origin is

P(x, y) = P'(y, -x)

The coordinates of T' = (-8, -4)

The coordinates of U' = (-8, -6)

The coordinates of V' = (-3, -9)

The coordinates of W' = (-3, -7)

Hence, The coordinates of the vertices after a rotation 270° counterclockwise around the origin is

T' = (-8, -4)

U' = (-8, -6)

V' = (-3, -9)

W' = (-3, -7)

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The length of the table is 1.51 meters.

Allan is measuring his dining room table to make a tablecloth. The table is 0.45 meter longer than it is wide. The width of the table is 1.06 meter. We need to find out the length of the table.

Let the length of the table be represented by the variable "L". In the context of a mathematical problem or experiment, a variable is a quantity that may vary. The length of the table is the sum of the width of the table and the difference between the two quantities.

L = 1.06 + 0.45

L = 1.51

Hence, the length of the table is 1.51 meters.

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Answer:  [tex]y=\frac{3}{4} x[/tex]

Step-by-step explanation:

        We will create a point-slope equation to solve.

        First, we need to find the slope.

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}= \frac{6--3}{8--4} =\frac{9}{12} =\frac{3}{4}[/tex]

        Next, we will create our point-slope equation.

[tex]\displaystyle y-y_1=m(x-x_1)[/tex]

[tex]\displaystyle y--3=\frac{3}{4} (x--4)[/tex]

 [tex]\displaystyle y+3=\frac{3}{4} (x+4)[/tex]

 [tex]\displaystyle y=\frac{3}{4} x+3 -3[/tex]

 [tex]\displaystyle y=\frac{3}{4} x[/tex]

The strategy which would eliminate a variable in the system of equations is to multiply the top equation by 6 ,multiply the bottom equation by -5 then add the equation and is denoted as option B.

This is a mathematical term which is made up of two expressions and is connected by an equal sign.

In the example given below:

8x + 5y = -7

-7x + 6y = -4

We can multiply the top by 6 and the bottom by -5 which will result in:

48x + 30y = -42

35x - 30y = 20

They are then added to each other to give:

48x + 35x + 30y - 30y = -42 + 20

83x = - 22

x = -22/83

From this we can notice that the variable y was eliminated which is why option B is the correct choice.

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Answer:

Step-by-step explanation:

When x varies inversely as the square root of y, and x=1 when y=4, you want to find ...

The given relation can be written using a constant of proportionality as ...

  x = k/√y  . . . . x varies as the inverse of the square root of y

The value of k can be found from the given values for x and y:

  1 = k/√4 = k/2

  2 = k . . . . . . . . . multiply by 2

The relationship between x and y can be written as ...

  x = 2/√y

Solving for y, it can also be written as ...

  y = 4/x²

The value of x is ...

  x = 2/√9

  x = 2/3

The value of y is ...

  y = 4/12² = 4/144

  y = 1/36

[tex]{\sf{ \frac{10}{50} = \frac{y}{125} \\ →50y = 10 \times 125 \\→ y = 25}}[/tex]

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Each of Aaron's pals receives nine (9) rocks in total.

The question states that,

Aaron collects a total of 54 rocks at the beach.

He wants to give an equal number of rocks to six (6) of his friends.

It is given that let 'r' be the number of rocks each of his friends gets.

The required equation is;

Rock's Aaron's friends get,

→ 6*r = 54

   r = 54/6

   r = 9

The total number of rocks each of Aaron's friends get is 9.

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The equivalent equation of the equation, [tex]\frac{5x+6}{2}=3-(4x+12)[/tex] is 5x + 6 = -18 - 8x

Two equations are said to be equivalent when they have the same solution set.

Equivalent equations are algebraic equations that have identical solutions or roots.

Therefore, let's find the equivalent equation of the equation.

[tex]\frac{5x+6}{2}=3-(4x+12)[/tex]

Let's open the bracket on the right side

[tex]\frac{5x+6}{2}=3-(4x+12)[/tex]

[tex]\frac{5x+6}{2}=3 - 4x - 12[/tex]

[tex]\frac{5x+6}{2}=(-9-4x)[/tex]

cross multiply

5x + 6 = 2(-9 - 4x)

5x + 6 = -18 - 8x

5x + 8x = -18 - 6

13x = - 24

divide both sides by 13

x = - 24 / 13

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