Anna walked 8 miles in 3 hours. Juan walked 14 miles in 5 hours. Are these rates in proportion?

Answer:

$10 per hour. It takes 0.1 hours to earn $1

Step-by-step explanation:

E=10h

E=10 x 1

E=10

Carys earns $10 per hour.

E=10h

1=10h

1/10=10h/10

0.1=h

It takes Carys 0.1 hours to earn a dollar.

Answer:

See explanation

Step-by-step explanation:

A sixth grade silence club needs 180$ to pay for the tickets to a science museum.

1. Suppose there 15 students in the club, then each of them needs to pay

[tex]\dfrac{\$180}{15}=\$12[/tex]

This means each ticket costs $12.

2. Suppose each ticket cost $15, then there are

[tex]\dfrac{\$180}{\$15}=12[/tex] students in the club.

Final answer:

Explains the meaning and interpretations of 180 divided by 15 in the context of purchasing museum tickets for a silence club in a clear manner.

Explanation:

180 divided by 15 in this context means dividing the total amount needed for tickets by the number of equal cost tickets being purchased. Let's interpret this:

Hence, the quotient of 180 divided by 15 is 12, which means either 15 tickets are bought or 12 tickets with the total amount.

Answer:

7C

Step-by-step explanation:

[tex]14c^2=2*7*c*c\\35 c=5*7*c\\G.C.F.=7C[/tex]

Answer:

6

Step-by-step explanation:

I assume you mean GCF, greatest common factor.

First, write the prime factorizations for each:

18 = 2¹ × 3²

24 = 2³ × 3¹

Next, find what they have in common.  Both have a factor of 2¹ and 3¹.

GCF = 2¹ × 3¹

GCF = 6

The greatest common factor is 6.

Answer:

6

Step-by-step explanation:

18 = 1x18 2x9 3x6

24 = 1x24 2x12 4x6 3x8

Answer:

option (B) $61,422

Explanation:

Given the annual salary is $70,600

Percent of Contribution made from the income = 13%

Pretax Salary/Income is calculated by the formula, Salary – 13% of salary

Pretax income =

[tex]70600 - \frac{13}{100} \times 70600[/tex]

= 70600 – 9178 = 61422

Therefore whitney’s pretax income is $ 61422

Hence, option (B) is correct

Answer:

The correct answer is B. $61,422

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

the only one that has a cop of 15 is b

The two ordered pairs to show that the equation y = 15x represents the data are (1, 15) and (2, 30) option (B) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The linear equation is:

y = 15x

Plug x = 1

y = 15

Plug x = 2

y = 30

The two points are (1, 15) and (2, 30) which lie on the equation of the line y = 15x

Thus, the two ordered pairs to show that the equation y = 15x represents the data are (1, 15) and (2, 30) option (B) is correct.

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Answer:

10n -11 =3 + 4n + 6n​

10n - 10n -11 =3-3 + 4n + 6n​

-11 - 3 = -10n + 4n + 6n

-14= -10n + 10n

-14 = n

Step-by-step explanation:

10n -11 =3 + 4n + 6n​

10n - 10n -11 =3-3 + 4n + 6n​

-11 - 3 = -10n + 4n + 6n

-14= -10n + 10n

-14 = n

Answer:

[tex]a=0.5[/tex]

[tex]b=-2[/tex]

Step-by-step explanation:

we have

[tex]y=ax^{2}+bx+3[/tex]

For x=2, y=1

substitute

[tex]1=a(2)^{2}+b(2)+3[/tex]

[tex]4a+2b=-2[/tex] -----> equation A

Remember that

If the function has a relative minimum in (2,1), then the first derivative of the function must be equal to zero when x=2

The first derivative is equal to

[tex]\frac{dy}{dx}=2ax+b[/tex]

so

[tex]0=2a(2)+b[/tex]

[tex]b=-4a[/tex] ----> equation B

Solve the system of equations A and B by substitution

Substitute equation B in equation A

[tex]4a+2(-4a)=-2[/tex]

solve for b

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

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

[tex]a=0.5[/tex]

Find the value of b

[tex]b=-4a[/tex] ----> [tex]b=-4(0.5)=-2[/tex]

The quadratic equation is

[tex]y=0.5x^{2}-2x+3[/tex]

Answer:

Liliana can make two batches of brownies!

Step-by-step explanation:

12/8 is equal to 6/4, which is double 3/4.

Liliana can make 2 batches of brownies.

12/8 is equal to 6/4

3/4 x 2 = 6/4

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Answer:

1.415 gram of the element will be left.

Step-by-step explanation:

The decay of radioactive element Krypton-91 can be formulated as  

[tex]A_{t} = A_{0} e^{-kt}[/tex] ............ (1)

where, [tex]A_{0}[/tex] is the initial amount of the element.

[tex]A_{t}[/tex] is the amount of element left after t seconds.

And k is a rate constant.

Now, given that the half-life of the element is 10 seconds.

So, from equation (1) we get

[tex]0.5 = e^{- k \times 10}[/tex]

taking ln on both sides, we get.

ln 0.5 = -10k

⇒ k = 0.0693

So, the equation (1) becomes [tex]A_{t} = A_{0} e^{-0.0693t}[/tex] ........ (2)

Now, if 16 gram of the element are initially present, then we asked to determine the amount of the element left after 35 seconds.

So, from equation (2) we have [tex]A_{t} = 16 e^{- 0.0693 \times 35} = 1.415[/tex] gm.

So, 1.415 gram of the element will be left. (Answer)

After 35 seconds, approximately 1.414 grams of krypton-91 would remain, based on its half-life of 10 seconds and the nature of radioactive decay.

The question pertains to the concept of radioactive half-life, which is the time it takes for half the atoms in a radioactive sample to decay. For krypton-91 with a half-life of 10 seconds, after 35 seconds, we can calculate the remaining amount using the concept of half-lives. We know that after each half-life, the remaining amount of the radioactive substance is halved.

To find out how many half-lives have passed in 35 seconds for krypton-91, we divide the elapsed time by the half-life:

Number of half-lives = Total time elapsed / Half-life duration = 35 seconds / 10 seconds = 3.5 half-lives.

After each half-life, the quantity remaining is halved. This gives us:

Amount after 1st half-life = 16 g / 2 = 8 g

Amount after 2nd half-life = 8 g / 2 = 4 g

Amount after 3rd half-life = 4 g / 2 = 2 g

However, since we have 3.5 half-lives, we must halve the amount one more time, but only halfway (since we have half of a half-life), giving us:

Amount after 3.5 half-lives = 2 g / √2 ≈ 2 g / 1.414 = 1.414 g

Therefore, approximately 1.414 grams of krypton-91 would remain after 35 seconds.

Answer:

The number of soda can that are in the pack is 6 .

Step-by-step explanation:

Given as :

The volume of soda pack = 113.04 inches³

The height of cylinder shaped can = H = 6 inches

The diameter of cylinder shaped can = 2 inches

So, the radius R = [tex]\frac{Diameter}{2}[/tex] =  [tex]\fr{2}{2}[/tex]

Or, R = 1 inches

Now, The volume of cylinder = [tex]\pi[/tex] × R² × H

Or , The volume of cylinder = 3.14 × 1² × 6

Or , The volume of cylinder = 3.14 × 6 = 18.84 inches³

So, The number of soda cans packed = [tex]\dfrac{\textrm volume of soda pack}{\textrm volume of cylinder}[/tex]

or,  The number of soda cans packed = [tex]\frac{113.04}{18.84}[/tex]

∴ The number of soda cans packed = 6

Hence The number of soda can that are in the pack is 6 .  Answer

Answer:

d < -28

d ∈ (-∞ , -28)

Step-by-step explanation:

[tex]\frac{d}{7}[/tex] + 4 < 0

Taking 4 on the right side of the equation,

We get,    [tex]\frac{d}{7}[/tex] < -4

Now, since 7 is positive number , we can transfer it to right side of the equation multiplying with -4,

It gives,  d < -28.

So  d belongs from -∞ to -28 excluding -28 ,

We can write, d ∈ (-∞ , -28).

Answer:

C

Step-by-step explanation:

Let length of rectangle be "l"

Let width of rectangle be "w"

We know,

LENGTH is 2 MORE THAN WIDTH, we can write:

l = w + 2

Also, note the perimeter is the sum of all 4 sides of a rectangle, thus:

length + width + length + width

Now,

The perimeter is given as 72, so we can write:

l + l + w + w = 72

2l + 2w = 72

We have 2 equations that we need to solve and find the length (l).

The first equation is:

l = w + 2

Rearranging, we have:

w = l - 2

We put this into 2nd equation and find the value of l:

[tex]2l + 2w = 72\\2l + 2(l-2) = 72\\2l+2l-4=72\\4l-4=72\\4l=76\\l=\frac{76}{4}\\l=19[/tex]

The length is 19 meters, the correct answer is C

Answer:

Tory=14 Quentin=14

Step-by-step explanation:

Sister and brother same age

s=sister    b= brother

 s=b

Tory=s+3    Quentin =2b-8 = 2s-8

EQUATION

s+3 = 2s-8

3=s-8

11=s

sister=11   brother = 11

Tory=11+3=14           quentin=2(11)-8 = 22-8=14

By creating equations based on the ages of Tory and Quentin relative to their siblings, we find that both Tory and Quentin are 14 years old.

Let's denote Tory's age as T and her sister's age as S. Given that Tory is 3 years older than her sister, we can write the first equation as:

T = S + 3

Similarly, let's denote Quentin's age as Q and his brother's age as B. It's given that Quentin's age is 8 years less than twice his brother's age, which gives us the second equation:

Q = 2B - 8

Since Tory and Quentin are the same age, we also know that T = Q, and their siblings are the same age, so S = B. Combining these equations:

T = S + 3
T = 2S - 8

Setting the two expressions for T equal to each other gives us:

S + 3 = 2S - 8

Solving this equation:

Tory and Quentin are both 14 years old.

Answer:

5 1/12

Step-by-step explanation:

What you should do is find the common denominator for all of these numbers, which is 12.

Now you have to multiply the fraction part so the denominator equals 12.

1*6/2*6= 6/12

3*3/4*3= 9/12

5*2/6*2= 10/12

Now you have to add up all of these numbers

2+6/12+1+9/12+10/12= 3 25/12, which simplified would equal 5 1/12.

Answer:

1

Step-by-step explanation:

8/2*4=8/8=1

Answer:

4. All of the values are not proportional except 2 values

5. All of the values are non-proportional

6. All of the values are proportional

7. The two variables are proportional when, (no. of pies ordered (one of the variables)) is ≥ 12 . but the two variables are non-proportional when, 0 < (no. of pies ordered (one of the variables))  < 12.

Step-by-step explanation:

4.All of  the values in table 4. are not proportional, except 2 since,

[tex]\frac {1}{17.25} = \frac{4}{70} \neq \frac{2}{35.50}  \neq \frac{3}{50.75}[/tex]

although the units for all fractions is the same i.e.,  hour/dollar

5. All  of the  values in table 5 are non-proportional since,

[tex]\frac {1}{37} \neq \frac {2}{73} \neq \frac {3}{109} \neq  \frac{4}{145}[/tex]

although units for all the fractions are the same. i. e., hour/no. of pages

6. All  of the values of the table 6. are proportional, since,

[tex]\frac {1}{2.75} = \frac {2}{5.5} = \frac {3}{8.25} = \frac {4}{11}[/tex]

and all of the fractions  have same unit i. e.,   number of lunches/dollar

7. If no, of pies ordered is less than a dozen, then the cost is given by,

 y = 5 + 4.5x    [y in $, where x is the no. of pies ordered and 0 < x < 12]

clearly, y is not proportional to x.

The table of some values is given by,

   x          y

   1          $ 9.5

   2          $  14

   3          $ 18.5                         etc.

If no, of pies ordered ≥ 12, then the cost is given by,

   m = 4.5n [m in $, where, n is  no. of pies ordered and n ≥ 12]

clearly, m is proportional to n

The table of some values is given by,

  n               m

  12             $ 54

  13              $ 58.5            

  14              $ 63                      etc.

Answer:

c

Step-by-step explanation:

Solve the inequality, that is

18 > 3x - 3 ( add 3 to both sides )

21 > 3x ( divide both sides by 3 )

7 > x, hence

x < 7

< is denoted by an open circle on the number line at 7, meaning that x cannot be equal to 7. Since less than 7 then the arrow head points to the left of 7

This is represented by Graph c

Answer:

$10

Step-by-step explanation:

Interest rate of 6% means ,She had to pay 6 percent of $400 in a year as Interest

Which is 6×[tex]\frac{400}{100}[/tex] = $ 24 (In 12 months)

So, In one month she had to pay $2.

Thus,

In 5 months she had to pay $10 as Interest

Answer: $10

Step-by-step explanation:

Formula for calculating interest= PRT ÷ 100 where,

P = Principal

R = Rate

T = Time

P= $400

R= 6%

T = 5 months

Note that there are 12 months in a year.

Simple Interest= PRT/100

= (400 × 6 × 5) ÷ (12 × 100)

= 12000 ÷ 1200

= 10

The simple interest is $10

Answer:

Because it is a rectangle, the area is expressed as A = xy, or length times width.

Because it is next to the river, he only needs to fence three sides, so F = x + 2y.

Knowing the amount of fencing available is 7500m, we get:

7500 = x + 2y        solve for x

x = 7500 - 2y         substitute into the area equation

A = (7500 - 2y)y     distribute

A = -2y2 +7500y

You can see that this is a parabola which opens down, meaning that the point of maximum area will be at the vertex, y = -b/2a = -7500/[2(-2)] = 1875

x = 7500 - 2(1875) = 3750

A = 3750(1875)  = 7,031,250 m2

Step-by-step explanation:

The largest area that can be enclosed is  781250 m²

where

l = length

w = width

The farmer wants to enclose a rectangular plot that borders a river. He is not fencing the side along the river. Therefore,

perimeter = l + 2w

l = 2500 - 2w

Therefore,

area = (2500 - 2w)w

(2500 - 2w)w = 0

w = 0 or 1250

average = 1250 / 2 = 625 meters

Hence, the max area is at w = 625 meters

Therefore,

l = 2500 - 2(625) = 1250

length = 1250 meters

width = 625 meter

Therefore,

area = 1250 × 625 = 781250 m²

Therefore, the largest area that can be enclosed is  781250 m²

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Answer:

7.92

Step-by-step explanation:

0.99*8=7.92

Answer:

8a = 8(.99)

7.92

hoope it helps

Answer:

4x

Step-by-step explanation:

5x+2x=7x

7x-3x=4x

Answer: 6

Step-by-step explanation: 5-2+3

A consistent , independent system of equation is one that has at least one solution.It is independent because it has a single solution.

Step-by-step explanation:

The three types of systems of linear equations in two variables and three types of solutions.

An independent  system has exactly one solution pair (x,y). The point of intersection presents the single solution.

An inconsistent system has no solution.such equations will produce two parallel lines with no solution.

A dependent system has infinitely many solution.Such lines are coincident.

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Keyword : consistent, independent , equations

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A consistent, independent system of equations is a system where the equations have a unique solution.

A consistent, independent system of equations is a system where the equations have a unique solution. This means that there is exactly one set of values for the variables that satisfy all of the equations simultaneously.

For example, consider the following system of equations:

In this system, there is a unique solution: x = 2 and y = 3. Therefore, it is a consistent, independent system of equations.

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Answer:

3

Step-by-step explanation:

3+11t-9u

3+11(9)-9(11)

3+99-99

3+0

3

Answer:

Step-by-step explanation:

3+11(9)-9(11)

3+99-99

3

Answer:

72

Step-by-step explanation:

3(20+4)=a0

60+12=a0

72=a0

im not quite sure what you want. I solved for a0. Plz tell me if this is correct. If its not, tell me what u need, then I will solve it for you.

Answer:

72

Step-by-step explanation:

3 * 20 = 60

3 * 4 = 12

60 + 12 = 72

Answer:

1.4 times k

Step-by-step explanation:

If k feet is the distance from home plate to third base, and the distance from first base to third base is 1.4 times the previous value, then

distance from first base to third base = 1.4 * k or 1.4 times k

If, for example, k=90 feet, then from first to third base there are

1.4*90=126 feet

Answer:

$38.00

Step-by-step explanation:

164/4=41          41-3=38

Answer:

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

Step-by-step explanation:

the y intercept is 0