When a 49 pound weight is attached to a spring, the spring stretches 7 inches. Assume that the length of the spring y varies directly
with the weight attached x. Write and solve a direct variation equation to
find the length of the spring when a 63 pound weight is attached.

Answer:

The cost of total lunch is 1.18 y ( 1+ 0.0 x )

Step-by-step explanation:

Given as :

The percentage of tip added tot he bill after tax = 18 %

Let the tax added to the bill = x % of total the lunch price

Let The total lunch cost = y

So, The cost of the lunch after tax = y + x %  × y

I.e The cost of lunch after tax = y × ( 1 +x % )

Or. The bill of lunch after tax = y × ( 1 + 0.0 x )

Now the cost of lunch after tax and tip =18 % of y × ( 1 + 0.0 x ) + y × ( 1 + 0.0 x )

Or, the cost of lunch after tax and tip =  y × ( 1 + 0.0 x ) (0.18 + 1 )

∴ The cost of lunch after tax and tip =  y × ( 1 + 0.0 x ) × 1.18

Hence The cost of total lunch is 1.18 y ( 1+ 0.0 x )  Answer

Answer:

The surface area of right prism is 12 feet²  , option D

Step-by-step explanation:

Given as :

The measure of base = 4 ft

The height of base = 0.5 ft

The surface area of right prism = perimeter of base × height + 2 × base

Now ,

Perimeter of base = 4 + 4 = 8 ft

So, The surface area of right prism = 8 × 0.5 + 2 × 4

Or, The surface area of right prism = 4 + 8

∴ , The surface area of right prism = 12 feet²

Hence The surface area of right prism is 12 feet²  . Answer

Answer:

17.5 ft2

Step-by-step explanation:

Answer:

9 sides!

Step-by-step explanation:

Nonagon has it's each interior angle measure as 140 degrees.

Polygon with 9 sides!

Answer:

314 of the people attending the fun fair are people living in the neighborhood

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Number of people attending the fun fair = 2,512

Fraction of people attending the fun fair that are students = 5/8

Fraction of people attending the fun fair that are parents = 1/4

Rest of the people attending the fun fair lives in the neighborhood

2. Let's calculate the number of students, parents and people living in the neighborhood

Students:

Fraction of people attending the fun fair that are students = 5/8

5/8 * 2,512 = 1,570

1,570 of the people attending the fun fair are students

Parents:

Fraction of people attending the fun fair that are parents = 1/4

1/4 * 2,512 = 628

628 of the people attending the fun fair are parents

People living in the neighborhood

2,512 - 1,570 - 628 = 314

314 of the people attending the fun fair are people living in the neighborhood

Answer:

[tex](4-\sqrt{19},4+\sqrt{19)[/tex]

Step-by-step explanation:

we have

[tex]x^{2} -8x=3[/tex]

Divide the coefficient of term x by 2

[tex]-8/2=-4[/tex]

Squared the number

[tex](-4)^2=16[/tex]

Adds the number 16 to the both sides

[tex]x^{2} -8x+16=3+16[/tex]

[tex]x^{2} -8x+16=19[/tex]

Rewrite as perfect squares

[tex](x-4)^{2}=19[/tex]

take square root both sides

[tex](x-4)=(+/-)\sqrt{19}[/tex]

[tex]x=4(+/-)\sqrt{19}[/tex]

[tex]x_1=4(+)\sqrt{19}[/tex]

[tex]x_2=4(-)\sqrt{19}[/tex]

therefore

The solution set is

[tex](4-\sqrt{19},4+\sqrt{19)[/tex]

Answer:

its A

Step-by-step explanation:

One hot dog costs $1.75 and one hamburger costs $2.25

Step-by-step explanation:

Let,

Hot dog = x

Hamburger = y

According to given statement;

7x+2y=16.75   Eqn 1

2x+7y=19.25   Eqn 2

Multiplying Eqn 1 by 2;

[tex]2(7x+2y=16.75)\\14x+4y=33.50\ \ \ Eqn\ 3[/tex]

Multiplying Eqn 2 by 7;

[tex]7(2x+7y=19.25)\\14x+49y=134.75\ \ \ Eqn\ 4[/tex]

Subtracting Eqn 3 from Eqn 4;

[tex](14x+49y)-(14x+4y)=134.75-33.50\\14x+49y-14x-4y=101.25\\45y=101.25[/tex]

Dividing both sides by 45;

[tex]\frac{45y}{45}=\frac{101.25}{45}\\y=2.25[/tex]

Putting y=2.25 in Eqn 1

[tex]7x+2(2.25)=16.75\\7x+4.50=16.75\\7x=16.75-4.50\\7x=12.25[/tex]

Dividing both sides by 7;

[tex]\frac{7x}{7}=\frac{12.25}{7}\\x=1.75[/tex]

One hot dog costs $1.75 and one hamburger costs $2.25

Keywords: linear equations, subtraction

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By using a system of linear equations, the cost of one hamburger is computed to be $2.25 and the cost of one hot dog is computed to be $1.75.

This question involves the use of a system of linear equations to solve for the cost of one hot dog and one hamburger. Let us denote the cost of one hot dog as 'd' and the cost of one hamburger as 'h'. We are given two equations from the problem: 7d + 2h = 16.75 and 2d + 7h = 19.25. Now we can solve this system for values of 'd' and 'h'.

First, we can multiply the first equation by 2 and the second by 7 to make the coefficients of 'h' the same in each equation: 14d + 4h = 33.5 and 14d + 49h = 134.75.

Subtracting the first equation from the second gives us 45h = 101.25. Finally, dividing both sides by 45, we find that h = $2.25 which is the cost of one hamburger.

Substitute h = $2.25 back into the first equation: 7d + 2($2.25) = 16.75. Simplifying, we get 7d = $12.25, and dividing both sides by 7 gives us d = $1.75 which is the cost of one hot dog.

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Answer:

We call a 21-sided polygon a Henacosagon.

Explanation:

See chart above

* 9 − nona-

I am joyous to assist you anytime.

The name of a 21 sided polygon is Henicosagon.

A polygon is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. The interior of a solid polygon is its body.

Given that, what is the name of a 21 sided polygon,

Polygons have very simple names for the first twenty names.

They use a basic prefix naming system. Di, tri, tetra, penta, and so on.

But polygons with 21 to 99 sides have a different naming system.

First, we use a prefix for the tens (such as triaconta—30). Then we use a prefix for the ones (such as di—20).

At last, we put them together with a ‘kai’ between them. This would be formatted to look like (tens)kai(ones)gon.

In simpler words, a 32-sided polygon. We can normally refer to it as a 32-gon.

Hence, the name of a 21 sided polygon is Henicosagon.

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Answer:

B

Step-by-step explanation:

Given

3x > 6 ( divide both sides by 3 )

x > 2

> is denoted by an open circle at 2 on the number line, meaning that x cannot equal 2. Since values are greater than 2 then numbers to the right of 2 are shaded.

This would be represented by graph B

Answer: B.) Open circle on 2 and all the numbers to the right are shaded

Step-by-step explanation:

The given inequality : [tex]3x>6[/tex]

Divide both sides by 3 , we get

[tex]x>2[/tex]

i.e. x is a numerical value strictly greater than 2 i.e. 2 is not-included.

When we plot this inequality on Number line , we starts with an open circle on 2 that signifies that 2 in not included and shade on the right side because x is greater than 2 which lies on the right side of 2 .

Hence, the correct answer is B.) Open circle on 2 and all the numbers to the right are shaded .

Answer:

7 units

Step-by-step explanation:

count

Answer:

7

Step-by-step explanation:

We use the Pythagorean theorem with a=1 and b=7.

c ≈ 7

Answer: 3 and 2/3

Step-by-step explanation: To subtract mixed numbers, first subtract the fractions.

Notice here however that we have 1/3 - 2/3 which will gives us a negative fraction. Since this will cause us a lot of trouble, instead, we can rewrite the first mixed number. We can do this by thinking of 6 and 1/3 as 5 + 1 and 1/3 or as 5 + 4/3 by changing 1 and 1/3 into an improper fraction.

So 6 and 1/3 can be written as 5 and 4/3.

Now we have 5 and 4/3 - 2 and 2/3.

Now, subtract the fractions.

So we have 4/3 - 2/3 which is 2/3. Then subtract the whole numbers. 5 - 2 is 3 and now we have the mixed number 3 and 2/3 which is in lowest terms.

Therefore, 6 and 1/3 - 2 and 2/3 = 3 and 2/3.

Since both fractions have common denominators we can just put them into improper fractions.

6 1/3 = 19/3

2 2/3 = 8/3

Now, we can subtract. (When you add or subtract fractions you only add or subtract the numerators, never the denominators.)

19/3 - 8/3 = 11/3

Turn into mixed number.

11/3 → 3 2/3

______

Best of Luck,

Wolfyy :)

Answer:

Improper Fraction- 5.9= 59/10

Mixed number-  5 9/10

Step-by-step explanation:

The mixed fraction of 5.9 is equal to  [tex]5\frac{9}{10}[/tex].

The given decimal number is,

5.9

We have to convert it into mixed fraction,

In order to get mixed fraction first of all convert it into fraction.

Since we know that,

A mixed fraction is one that is created by mixing a whole number and a proper fraction.

Now multiply and divide this with 10 we get,

5.9 = (5.9x10)/10

      = 59/10

Now proceed it by long division method,

10 ) 59 ( 5

   -  50

______

         9

Hence, the mixed fraction of the given number is,

⇒ 5.9 = [tex]5\frac{9}{10}[/tex]

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Answer:

y-3=3/5x

Step-by-step explanation:

y-y1=m(x-x1)

Where m=slope and (x1, y1) is a point on the line.

m=(y2-y1)/(x2-x1)

m=(0-3)/(-5-0)

m=-3/-5

m=3/5

y-3=3/5(x-0)

y-3=3/5(x)

y-3=3/5x

(0, 3) is the y-intercept as it passes through y = 3 at x = 0, or the y-axis.

Slope:

[tex] \frac{y1 - y0}{x1 - x0} = \frac{3 - 0}{0 - ( - 5)} = \frac{3}{5} [/tex]

Equation of a straight line:

y = mx + c

m = slope (3/5)

c = y value of y-intercept (3)

Equation:

[tex]y = \frac{3}{5} x + 3[/tex]

Answer:

The total number of Green team members is 160.

Step-by-step explanation:

Given 90% of the total members present at the meeting which is 144.

Let the total number of members be x.

[tex]90\%\ of x=144\\\frac{90\times\ x}{100}=144\\9x=1440\\x=\frac{1440}{9}=160[/tex]

Hence we can say that, The total number of Green team members is 160.

Answer:

160

Step-by-step explanation:

Answer:

a = 3

Step-by-step explanation:

b = 3

10*3 = 30

45-30 = 15

15/5 = a

a = 3

Answer:

15

Step-by-step explanation:

5a-10(3)=45

5a=45+30

5a=75

a=15

Answer:15.6

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

Given

9x - 43 = 5x + 1 ( subtract 5x from both sides )

4x - 43 = 1 ( add 43 to both sides )

4x = 44 ( divide both sides by 4 )

x = 11

Answer: the answer is B. 5p

Step-by-step explanation:

just did it so i know its right:)

comment if so!

There is no illustration, so it is impossible to answer this question. I apologize.

Answer:

4 times 7 time 4 = 112

Answer: GCF of 54 and 45: 9.

Step-by-step explanation: The factors of 54 include: 1, 2, 3, 6, 9, 18, 27, and 54. The factors of 45 include: 1, 3, 5, 9, 15, and 45. The largest common factor of 45 and 54 is 9.

the answer is 100....... ...

Answer:

Perimeter of trapezoid ABEF= 16x +4

Step-by-step explanation:

Since it is an equilateral triangle

AC = BC = BC = 7x - 2

Point E and F is formed at mid point of line AC and BC respectively.

Therefore AE = 1/2 x AC and BF = 1/2 x BC

Perimeter of trapezoid ABEF = AB + EF + AE + BF

AB = 7x - 2

EF = 2x + 8

AE = (7x - 2)/2

BF = (7x - 2)/2

Perimeter = 7x - 2 + 2x + 8 + (7x - 2)/2 + (7x - 2)/2

= 7x - 2 + 2x + 8 + 7x - 2

= 7x + 2x + 7x - 2 + 8 - 2

Perimeter of trapezoid ABEF= 16x + 4

There's a 16% probability that the air-conditioning unit will take longer than 25 minutes to cool a 2000-square-foot home by 1 degree on a 95-degree day with 80% humidity, based on the empirical rule of normal distribution.

To find the probability of the air-conditioning unit taking longer than 25 minutes to cool the house 1 degree, you first have to understand that the situation described follows a normal distribution with a mean (μ) of 24 minutes and a standard deviation (σ) of 1 minute.

Using the Empirical Rule, also known as the 68-95-99.7 rule, we can assess probabilities for normal distributions.

According to the Empirical Rule, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Since we are interested in the time more than 25 minutes, we are looking at the area to the right of the mean plus 1 standard deviation (24 + 1 = 25 minutes).

Approximately 68% of the data falls within one standard deviation (between 23 and 25 minutes), so about 34% is below 25 minutes, and another 34% is above. However, we're interested in the portion beyond 25 minutes, falling in the tail.

Because 50% of the distribution falls above the mean (by definition of a normal distribution), and we account for the 34% within one standard deviation above the mean, this leaves us with 50% - 34% = 16% of data points (times in this case) falling beyond 25 minutes on a 95-degree day with 80% humidity.

Answer:

2y-4-6y-12=4

-4y=20

y= -5

Step-by-step explanation:

because (y+2)(y-2)=y^2-4

so we have the step to let the every part have the same denominator y^2-4

2(y-2)/(y+2)(y-2)  -6(y+2)/(y-2)(y+2)=4/(y-2)(y+2)

the denominators are the same so the equality .we just need the part over be the same 2y-4-6y-12=4

y= -5

Answer:

160 member

Step-by-step explanation:

Here the question is, how many total member are there in the team?

Given: 144 member in the meeting is equal to 90% of the total group.

Let assume x be the total member in the green team.

Now, finding the number of member in the team, which is x.

[tex]\frac{90}{100} \times x = 144[/tex]

Next, cross multiply the number on both the side

⇒ [tex]x= \frac{144 \times 100}{90} = 16\times 10[/tex]

∴ x = 160

160 is the total number of member in green team.

Answer:

160 members

Step-by-step explanation:

How do I know this well 144/90 1.6 take away the decimal and it is 16 add a 0 from the 90 and 160

Answer:

8 times more 8*2 1/2 = 20 pounds.

Step-by-step explanation:

Answer:

20 pounds of grass seed is needed for one acre.

Step-by-step explanation:

You can set up a proportion to solve:

[tex]\frac{2.5 pounds}{1/8 acre}[/tex] = [tex]\frac{x pounds}{1 acre}[/tex]

Cross multiply:

[tex]\frac{1}{8}[/tex]x = 2.5

Divide both sides by [tex]\frac{1}{8}[/tex] or multiply both sides by 8.

x = 20

Answer:

C. 36π

Step-by-step explanation:

The formula for volume of a sphere is:

V=⁴/₃πr³

We are given diameter: 6

To convert to radius, divide by 2.

6÷2=3. R=3

Plug in to formula

V=⁴/₃π3³

Simplify with multiplication

V=⁴/₃π27

V=36π

Answer is 15.4 miles

Step-by-step explanation:

So she ran each day for a week and including the weekend is 7 days so if we do 7 times 2.20 it should equal 15.4 miles, also 2 1/5= 2.20 or 2.2 same thing.. Hope this helps, Also I hope I read the question right :/

The area will be 2522.60 km^2 after 11 years

Step-by-step explanation:

First of all, we have to form a funtion for the given scenario.

Let

A be the initial area

r be the decrease rate

and t be the time

Let A_n be the area after t years

Then the function can be given by:

[tex]A_n=A(1-r)^t[/tex]

Given

A=4700 km^2

r=5.5%

t=11 years

Putting the value of rate

[tex]A_n=4700(1-0.055)^t\\=4700(0.945)^t[/tex]

The function can be used to calculate the reduced area

Putting t=11

[tex]A_n=4700(0.945)^{11}\\=2522.596[/tex]

Rounding off to nearest hundredth

[tex]A_n=2522.60\ km^2[/tex]

The area will be 2522.60 km^2 after 11 years

Keywords: Area, Functions

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Final answer:

To find the forest area after 11 years with an annual decrease of 5.5%, the exponential decay formula can be applied using the initial forest area and the given rate of decrease.

Explanation:

The question is asking how to calculate the decrease in the forest area over a period of time using a fixed percentage decrease per year. We'll use the formula for exponential decay to find the forest area after 11 years, which is expressed by A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the rate of decrease, and t is the time in years.

To compute the forest area after 11 years with an annual decrease of 5.5%, we'll plug P = 4700 km², r = 0.055, and t = 11 years into the formula. Therefore, the calculation is as follows:

A = 4700 × (1 - 0.055)[tex]11^{2}[/tex]

= 5,37,421.5

After calculating the above expression, we will get the reduced forest area in square kilometers.

The value of f(-3) will be zero

Step-by-step explanation:

Given ordered pair of function f is:

(7,0) )(-3,0) (2,0)(9,0)

The general form of ordered pair is (x,y) where x is the element of domain of function and y is the respective range value i.e. x is input and y is output

So,

In order to find the value of f(-3) we have to observe which ordered pair has -3 as input i.e. as first element of ordered pair

The required ordered pair is: (-3,0)

In the required pair, -3 is the input and 0 is the respective output

So,

The value of f(-3) will be zero

Keywords: Domain, Range

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Since rectangle PQRS is rotated 90 clockwise about the origin what are the coordinates of R' are: A. R' (4, -1).

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).

By applying a rotation of 90° clockwise about the center (origin), the coordinates of triangle A'B'C' are as follows;

(x, y)                               →            (y, -x)

Coordinate P (-3, -1)    →  Coordinate P' (-1, 3)

Coordinate Q (-1, -1)     →   Coordinate Q' (-1, 1)

Coordinate R (-1, -4)     →   Coordinate R' (-4, 1)

Coordinate S (-3, -4)     →   Coordinate S' (-4, 3)

Complete Question:

Rectangle PQRS is rotated 90 clockwise about the origin. What are the coordinates of R'?