13. A point is ___
from two objects if it is the same distance from the objects.

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:

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

Step-by-step explanation:

the y intercept is 0

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:

Option D =[6    18]  is the correct answer

Step-by-step explanation:

Given that:

[4  2] * [-2    5; 7    -1]

For taking product:

= [4*-2 + 2*7    4*5 + 2*-1]

=[-8 + 14        20 + (-2) ]

=[6    18]

i hope it will help you!

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:

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:

$38.00

Step-by-step explanation:

164/4=41          41-3=38

Answer:

x>=-12

Step-by-step explanation:

3x+7>=-29

3x>=-29-7

3x>=-36

x>=-36/3

x>=-12

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:

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:

48

Step-by-step explanation:

2x-1=6

2x=6+1

2x=7

x=7/2

------------

4x^2-1

4(7/2)^2-1

4(49/4)-1

49-1

48

Answer: 48

Step-by-step explanation:

2x - 1 = 6

Add 1 to both sides of the equation , we have:

2x = 7

divide through by 2

x = 7/2

The value of [tex]4x^{2}[/tex] - 1 will be calculated by substituting in the value of x , that is

[tex]4x^{2}[/tex] - 1 = 4([tex](\frac{7}{2} )^{2}[/tex] - 1

= 4([tex]\frac{49}{4}[/tex]) - 1

= 49 - 1

= 48

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:

[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:

D)24 people

Step-by-step explanation:

Total number of people, x=300

Number of people donated blood with type A, y

[tex]=\frac{28}{100}\times x\\=\frac{28}{100} \times 300\\=84[/tex]

Number of people donated blood with type B, z

[tex]=\frac{20}{100}\times x\\=\frac{20}{100} \times 300\\=60[/tex]

⇒Number of people with Type A blood donated more than those with Type B blood= y-z=84-60= 24

Answer:

D) There are 24 more people who donated Type - A then Type -B.

Step-by-step explanation:

Total number of people who donated the blood in shelter = 300

Percentage of people who donated the type A = 28%

Percentage of people who donated the type B = 20%

Now, 28 %  of 300 = [tex]\frac{28}{100 } \times 300 = 84[/tex]

So, the total number of people who donated the Type - A  = 84 people.

Also, 20 %  of 300 = [tex]\frac{20}{100 } \times 300 = 60[/tex]

So, the total number of people who donated the Type - B  = 60 people.

So, the difference in the people who donated type A and Type B  

= Number of people who donated the {Type - A  - Type - B}

= 84 people -  60 people

= 24 people

or, the difference in the people who donated type A and Type B  = 24

Hence, there are 24 more people who donated Type - A then Type -B.

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:

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:

2x - y = 3.

Step-by-step explanation:

0.2x = 0.1y + 0.3

Multiply through by 10:

2x = y + 3

2x - y = 3.

Answer:

25 tickets were purchased ahead of time

Step-by-step explanation:

25(11)=275 which is the price of the 11 bought at the door then you  take 625-275=350 which is the amount of money that was raised through purchases ahead of time so you take 350/14=25 meaning that 25 tickets were bought ahead of time.

There are 25 tickets were purchased ahead of time.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The cost of tickets to a fundraiser when purchased ahead = $14

The cost of tickets to a fundraiser when purchased at the door = $25

And, The total amount raised from all ticket sales = $625

Now,

Let number of tickets to a fundraiser when purchased ahead = x

And, The number of tickets to a fundraiser when purchased at the

door = y

We can formulate;

⇒ $14x + $25y = $625

Since, The number of tickets to a fundraiser when purchased at the

door = 11

So, y = 11

Hence, We can formulate;

⇒ $14x + $25y = $625

⇒ $14x + $25 × 11 = $625

⇒ $14x + $275 = $625

⇒ $14x = $625 - $275

⇒ $14x = $350

⇒ x = 25

Thus, There are 25 tickets were purchased ahead of time.

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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:

P=0.39

Step-by-step explanation:

We use the Hypergeometric distribution to find the probability

The normal deck of cards has 52 cards, 26 red and 26 black

Taking 4 cards out of the whole deck can be done (without replacement) in

[tex]\begin{pmatrix}52\\4\end{pmatrix}[/tex]

different ways .

Taking 2 red cards can be done in

[tex]\begin{pmatrix}26\\2\end{pmatrix}[/tex]

different ways. Same applies to the black cards

So, the required probability can be computed as

[tex]P=\frac{\begin{pmatrix}26\\2\end{pmatrix}\begin{pmatrix}26\\2\end{pmatrix}}{\begin{pmatrix}52\\4\end{pmatrix}}[/tex]

[tex]{\begin{pmatrix}52\\4\end{pmatrix}}=\frac{52!}{4!48!}=270725[/tex]

[tex]{\begin{pmatrix}26\\2\end{pmatrix}}=\frac{26!}{2!24!}=325[/tex]

[tex]P=\frac{325x325}{270725}=0.39[/tex]

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:

The number of dimes = 32

The number of quarters  = 14

Step-by-step explanation:

Here, the total number of coins combined = 46

Let us assume the number of dimes = m

So, the Number of quarter = Total Coins - Number of dimes  = 46 - m

Now,as we know:

1 dime = $0.1

So, m dimes  = m x ($0.1) = $(0.1 m)

1 Quarter  = $0.25

So, ( 46 - m ) Quarters  = (46 - m ) x ( $ 0.25)   = 11.5 - 0.25 m

Also, given the total amount of coins = $ 6.70

⇒ Value of (Dimes + Quarters) = $ 6.70

or, (0.1 m) +  11.5 - 0.25 m  = 6.70

-0.15 m = - 4.8

or, m = 4.8/0.15  =  32

⇒ m = 32

Hence, the number of dimes = m = 32

And the number of quarters  = 46 - m= 46 -32 = 14

Answer:

4x

Step-by-step explanation:

5x+2x=7x

7x-3x=4x

Answer: 6

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

Answer:

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:

1

Step-by-step explanation:

8/2*4=8/8=1

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:

7.92

Step-by-step explanation:

0.99*8=7.92

Answer:

8a = 8(.99)

7.92

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