The chance that a positive response is obtained from Chicago fro program 1 is %. The chance that a positive response is obtained from Chicago for program 2 is %.

Answer:

Option A that is [tex]99.34[/tex] is the correct choice.

Step-by-step explanation:

To find what percentage of carbon-14 is still remaining after [tex]55[/tex] years.

We have to pull the equation and instead of [tex]t[/tex] we will put the years in numbers that is [tex]t=55[/tex]

Lets see the equation.

[tex]C(t)=100.e^{-0.000121(t)}[/tex]

Now to find the carbon-14 percentage.

Putting the value of [tex]t[/tex] in years.

So

[tex]C(t)=100.e^{-0.000121(t)}[/tex] and [tex]e^{-0.000121(55)}=0.9934[/tex]

[tex]C(t)=100\times 0.9934 =99.34[/tex]

As mentioned that the function is already framed to find the percentage we need not to convert it or multiply with [tex]100[/tex].

So the percentage of C-14 remaining after [tex]55[/tex] years is [tex]99.34[/tex]

Option A is the correct choice.

C: 4 is the right answer

Step-by-step explanation:

Given

a1 = -3

a15 = 53

We know that explicit formula for the arithmetic sequence is:

[tex]a_n=a_1+(n-1)d[/tex]

For the 15th, term it will be

[tex]a_{15}=-3+(15-1)d\\53=-3+14d[/tex]

Adding 3 on both sides

[tex]53+3 = -3+3 + 14d\\56 = 14d[/tex]

Dividing both sides by 14

[tex]\frac{56}{14}=\frac{14d}{14}\\d=4[/tex]

Hence,

C: 4 is the right answer

Keywords: Arithmetic sequence, Common Difference

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Answer:

C) 4 is the correct answer

Answer: 1x = $8.06y

Step-by-step explanation:

thats honestly all i know..

Answer:

y+2x=9 is the line passing through (6,-3) parallel to y=-2x-5

Step-by-step explanation:

In the question we are given with a point (6,-3) and a line [tex]y=-2x-5[/tex]. we have to find the line passing through given point and parallel to given line.\

formula used: equation of a line passing through a point(a,b) with slope m is given by [tex](y-b) = m(x-a)[/tex].

here we have (a,b)=(6,-3) and the slope of the line is slope of [tex]y=-2x-5[/tex]

i.e, -2( coefficient of x).

therefore,  substituting point and slope in formula we get [tex]y+3 = -2(x-6)[/tex]

which simplifies to [tex]y+3= -2x+12\\ y+2x=9[/tex] is asked line equation

Answer: 25

Step-by-step explanation: This problem states that the sum of four consecutive whole numbers is 94 and it asks us to find the largest number.

Three consecutive whole numbers can be represented as followed.

X ⇒ first number

X + 1 ⇒ second number

X + 2 ⇒ third number

X + 3 ⇒ fourth number

Since the sum of our four consecutive whole numbers is 94, we can set up an equation to represent this.

X + X + 1 + X + 2 + X + 3 = 94

We can combine the x's on the left side of the equation and combine the numbers as well.

4x + 6 = 94

      -6    -6   ← subtract 6 from both sides of the equation

4x = 88

÷4    ÷4

X = 22

X ⇒ first number   = 22

X + 1 ⇒ second number   = 23

X + 2 ⇒ third number   = 24

X + 3 ⇒ fourth number   = 25

Therefore, the largest number would be 25.

Answer:

three fourth mile=[tex]\frac{3}{4} mile[/tex]

Step-by-step explanation:

Given

⇒

[tex]\text{Distance from house to store}=\frac{1}{3} \times \text{Distance from house to friends house}\\ \text{Distance from house to friends house}= 3\times \frac{1}{4}\\ \text{Distance from house to friends house}=\frac{3}{4}[/tex]

Distance from her house to friends house  [tex]\frac{3}{4}[/tex] miles

Answer:

12

Step-by-step explanation:

h(x) = f(g(x))

Using chain rule:

h'(x) = f'(g(x)) g'(x)

h'(1) = f'(g(1)) g'(1)

h'(1) = f'(2) g'(1)

h'(1) = -4 × -3

h'(1) = 12

Answer: 3

Step-by-step explanation:

Given : A manufacturer of window frames knows from past experience that 15 per cent of the production will have some type of minor defect that will require adjustment.

i.e. the proportion of production will have some type of minor defect that will require adjustment. : p=0.15

If n=20 windows are selected at random , then the expected number of window frames have minor defects = np

[tex]=20\times0.15=3[/tex]

Hence, the expected number of window frames have minor defects =3

Answer:

The speed of faster bus is 108 kmph and The speed of slower bus is 98 kmph  .

Step-by-step explanation:

Given as :

The two buses apart 1442 km

The time taken for apart = 7 hours

Let The speed of faster bus = x kmph

The speed of slower bus = ( x - 10 ) kmph

Now Speed = [tex]\dfrac{\textrm distance}{\textrm time}[/tex]

∵ Both the buses traveling in opposite direction

So, The speed of faster bus + the speed of slower bus =  [tex]\dfrac{\textrm distance cover}{\textrm time}[/tex]

Or, x + x - 10 = [tex]\frac{1442}{7}[/tex]

or, 2 x = 206 + 10

or, 2 x = 216

∴  x = [tex]\frac{216}{2}[/tex]

I.e x = 108  kmph

So, The speed of faster bus = x = 108 kmph

And The speed of slower bus = ( x - 10 ) = 108 - 10 = 98 kmph

Hence The speed of faster bus is 108 kmph and The speed of slower bus is 98 kmph  . Answer

Answer:

8.80

Step-by-step explanation:

Final answer:

To round 8.795 to the nearest cent, look at the third decimal place. Since it's 5 or greater, round up the second decimal place to get 8.80.

Explanation:

When rounding 8.795 to the nearest cent, the focus is on the hundredth's place, since a cent is one hundredth of a dollar. You look at the digit in the thousandth's place to decide whether to round up or down. The digit in the thousandth's place is a 5, which means we follow the rule to round up since it is greater than 5. Thus, rounding 8.795 to the nearest cent gives us 8.80.

Answer:

[tex]P=4x+10[/tex]

Step-by-step explanation:

Let

x -----> the length of Danielle's board in feet

y ----> the length of Tracy's board in feet

we know that

[tex]y=x+5[/tex] ----> equation A

The perimeter of the sandbox is equal to

[tex]P=2(x+y)[/tex] ----> equation B

substitute equation A in equation B

[tex]P=2(x+x+5)[/tex]

[tex]P=2(2x+5)[/tex]

[tex]P=4x+10[/tex]

Answer:

The total volume of the solid is 1.67 cubic units.

Step-by-step explanation:

Each pyramid with a height of 2 units and a rectangular base with dimensions of 5 units × 0.25 units.

Therefore, the volume of each pyramid will be [tex]\frac{1}{3} \times \textrm {(Area of base rectangle)} \times \textrm {Height}[/tex]

= [tex]\frac{1}{3} \times (5 \times 0.25) \times 2 = 0.833[/tex] cubic units.

So, the total volume of the solid is (2 × 0.833) = 1.67 cubic units. (Answer)

Final answer:

To calculate the volume of the composite figure made from two identical pyramids with rectangular bases, we first find the volume of one pyramid using the formula for the volume of a pyramid and then multiply by two, resulting in a total volume of 1.666 cubic units.

Explanation:

The question involves calculating the volume of a composite figure made of two identical pyramids attached at their bases, with each pyramid having a rectangular base. The dimensions provided are a height of 2 units for each pyramid, and the rectangle's sides are 5 and 0.25 units. To find the volume of one pyramid, we use the formula for the volume of a pyramid, V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. The area of the rectangular base, B, is calculated as length × width = 5 × 0.25 = 1.25 square units. Substituting the values into the volume formula gives us V = (1/3)×1.25×2 = (1/3)×2.5 = 0.833 cubic units for one pyramid. Since the composite figure is made up of two such pyramids, the total volume is 2 × 0.833 = 1.666 cubic units.

For this case we must find the solution set of the given inequalities:

Inequality 1:

[tex]3x + 10 <3[/tex]

Subtracting 10 from both sides of the inequality:

[tex]3x <3-10[/tex]

Different signs are subtracted and the major sign is placed.

[tex]3x <-7[/tex]

We divide between 3 on both sides of the inequality:

[tex]x <- \frac {7} {3}[/tex]

The solution is given by all values of x less than[tex]- \frac {7} {3}[/tex]

Inequality 2:

[tex]2x-5> 5[/tex]

Adding 5 to both sides of the inequality:

[tex]2x> 5 + 5\\2x> 10[/tex]

Dividing by 2 to both sides of the inequality:

[tex]x> \frac {10} {2}\\x> 5[/tex]

The solution is given by all values of x greater than 5.

Thus, the solution set is given by:

(-∞, [tex]- \frac {7} {3}[/tex]) U (5,∞)

ANswer:

(-∞, [tex]- \frac {7} {3}[/tex]) U (5,∞)

Answer:

The Total number of adults ticket's is 15

The Total number of Senior citizen ticket's is 5

Step-by-step explanation:

Given as :

The total number of movies tickets were bought = 20

The cost of adults tickets = $ 8.00

The cost of senior citizen tickets = $ 4.00

The total money spent on movie tickets = $ 140

Let The total number of adults tickets = A

And The total number of senior citizen tickets = S

Now, According to question

The total number of movies tickets were bought = 20

I.e The total number of adults tickets + The total number of senior citizen tickets = 20

Or, A + S = 20

And $ 8 A + $ 4 S = $ 140  .........1

I.e 8 × ( A + S ) = 8 × 20

Or, 8 A + 8 S = 160         .......2

Solving the equation 1 and 2

Or, (  8 A + 8 S ) - (  8 A + 4 S ) = 160 - 140

Or, (  8 A - 8 A ) + ( 8 S - 4 S ) = 20

or, 0 + 4 S = 20

∴ S = [tex]\frac{20}{4}[/tex]

I.e S = 5

So, The number of Senior citizen ticket's = 5

Put The value of S in eq 1

So,  8 A +  4 × 5 = 140

Or, 8 A = 140 - 20

Or, 8 A = 120

∴  A = [tex]\frac{120}{8}[/tex]

I.e A = 15

So, The number of adult's tickets = 15

Hence The Total number of adults ticket's is 15

And The Total number of Senior citizen ticket's is 5    Answer

The width of plot of land is 13/8 kilometers.

Step-by-step explanation:

Area of rectangular plot = 52/96 square kilometers

Length of plot = 4/12 kilometers

Width of plot = w

Area of rectangle = length * width

[tex]\frac{52}{96}=\frac{4}{12}*w\\[/tex]

Multiplying both sides by [tex]\frac{12}{4}\\[/tex]

[tex]\frac{52}{96}*\frac{12}{4}=\frac{12}{4}*\frac{4}{12}w\\\\\frac{624}{384}=w\\\\\frac{13}{8}=w\\\\w=\frac{13}{8}[/tex]

The width of plot of land is 13/8 kilometers.

Keywords: rectangle, area

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Answer:

One solution since x=0

Answer:

x + y ≥ 35 and 15x + 8y ≥ 350

Step-by-step explanation:

Mitch is packing books into boxes.

Each box can hold either 15 small books or 8 large books.

Now, given that Mitch needs to pack at least 35 boxes and at least 350 books.

Now, if x is the number of small book-boxes and y is the number of large book-boxes,

Then, we can write from the above conditions that

x + y ≥ 35.......... (1) and

{Since total number of boxes must be at least 35}

15x + 8y ≥ 350 .......... (2)

{Since the total number of books must be at least 350 and each large book-boxes contain 8 large books and each small book-boxes contain 15 small books}

Therefore, the equations (1) and (2) are the required inequality equations that model the situation. (Answer)

There are 20 players are on the team.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

On the middle school baseball team, 8 players are sixth graders.

And, Of the players, 40% are sixth graders.

Now,

Let number of players on the team = x

So, We can formulate;

⇒ 40% of x = 8

⇒ 40/100 × x = 8

⇒ 40x = 800

⇒ x = 800/40

⇒  x= 20

Thus, Number of players on the team = 20

Learn more about the percent visit:

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Final answer:

There are 20 players on the middle school baseball team in total, calculated by dividing the number of sixth graders (8) by the percentage that represents sixth graders (40%).

Explanation:

Based on the information given, if 40% of the players on the middle school baseball team are sixth graders, and there are 8 sixth graders on the team, we can calculate the total number of players on the team. We know that 40% is equal to 0.40 when expressed as a decimal. Thus, the equation to find the total number of players (T) is 0.40 * T = 8.

To find T, divide both sides of the equation by 0.40:

T = 8 / 0.40

T = 20

Therefore, there are 20 players on the team in total.

Answer:

$5

Step-by-step explanation:

10% = 10/100 = 1/10.

1/10 of 50 = 5

The solution for C in terms of D and W is:

[tex]C = \frac{W+4D}{3}[/tex]

Step-by-step explanation:

Solving a formula for a given variable means to isolate the variable on one side of the equation

Given equation is:

[tex]W = 3C-4D[/tex]

We have to solve for C in terms of W and D

Adding 4D on both sides

[tex]W+4D = 3C-4D+4D\\W+4D=3C[/tex]

Dividing both sides by 3

[tex]\frac{W+4D}{3}=\frac{3C}{3}\\C = \frac{W+4D}{3}[/tex]

So,

The solution for C in terms of D and W is:

[tex]C = \frac{W+4D}{3}[/tex]

Keywords: Formula, Variables

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Answer: 39.76

Step-by-step explanation: To find 56% of 71, first write 56% as a decimal by moving the decimal point two places to the left to get .56.

Next, the word "of" means multiply so we have .56 × 71.

(.56) (71) = 39.76

Therefore, 56% of 71 is 39.76.

Answer:

After that????? Please ask me the full question please.

Thank you

i have no idea how many apples should she sell

Answer:

She should sell 30 apples and 20 oranges

Step-by-step explanation:

3+2=5 so everytime she does that she gets another 5 fruit sold just add a 0 to both and boom 50. I hope thats right, im pretty sure it is

Answer:

I don't really know but I can maybe figure it out

Answer:

$285

Step-by-step explanation:

Blueberries:

B = number of pounds of blueberries bought

$5.50 = price of blueberries per pound

$5.50B = total price of B pounds of blueberries

Blueberries:

R = number of pounds of raspberries bought

$4 = price of raspberries per pound

$4R = total price of R pounds of raspberries

Total:

$5.5B + $4R

Since 5.5B+4R=285, then Amit spends in total on both types of berries $285

Complete question:

5B+4R=28

The above equation is true if Amit buys B pounds of blueberries and R pounds of raspberries at a farm where blueberries cost $5.50 per pound and raspberries cost $4.00 per pound. According to the equation, how much does Amit spend in total on both types of berries?

Answer:

In total Amits spends $28 in both types of berries.

Step-by-step explanation:

The equation is

5B+4R=28

B represent the weight in pounds of the blueberries and R represent the weight in pounds of the raspberries.

B =  weight in pounds of blueberries

R = weight in pounds of raspberries

The price per pound of blue berries is $5.50. The amount of blueberries he takes depending on the number of pounds Amit buys which is equals to 5B.

Cost of blueberries depending on the number of pounds = 5.5B

The price per pound of the blue berries is $4.00 .The cost of raspberries he takes depend on the number of pounds Amit buys which is equal to 4R.

Cost of raspberries depending on the number of pounds = 4R

The total cost of both blueberries and raspberries depending on the number of pounds is equals to 5B+4R=28

Total cost

5B+4R=28

In total Amits spends $28 in both types of berries.

Step-by-step explanation: In this problem, we are asked to find the volume of a box which means we use the formula for finding the volume of a rectangular prism.

To find the volume of a rectangular prism or a prism whose base is a rectangle, we use the following formula.

Volume = length × width × height

Before plugging any numbers into our length, width, or height, first notice that we have dimensions in inches and feet. To make this easier, let's first convert the width which is 1.5 feet into inches. 1.5 feet is equal to 18 inches so now we are all set.

Since the rectangular prism has a length of 14 inches, a width of 18 inches, and a height of 7 inches, we can plug this information into the formula.

Volume = (14 in.) (18 in.) (7 in.)

Volume = 1,764 in.³

Therefore, the volume of the box is 1,764 in.³.

Answer:

8 pounds per tablespoon

Step-by-step explanation:

2 (3) = 6

48 (1/6) = 8

Answer:

8 pounds per tablespoon

Step-by-step explanation:

2 (3) = 6

Step-by-step explanation:

Answer:

Brett is 62 years old,    Mark is 80 years old     and Carl is  70 years old

Step-by-step explanation:

First; we let Brett age to be  = x

let  Mark age to be = y

let Carl age to be = z

From the question;

since Brett is 18 years younger than Mark, then Brett age is ;

x =  y - 18

Also, since  Carl is 10 years older younger than Mark, then Carl age is:

z   =   y-10

Also, from the question says  the sum of the ages of Brett, Mark and Carl is 212

This means when you add all their ages together, you will have 212

so;         x   +   y  +  z    =   212

From the equation above, we can substitute x with y-18 and then substitute z with y-10

y-18   +   y     +     y-10     =  212

3y   -  28    =    212

add 28 to both-side of the equation

3y   - 28   + 28   =    212  +   28

3y    =  240

Divide both-side of the equation by 3

3y/3   =   240/3

y   =   80

But x = y -18   =   80 -18  =   62

Also;   z =  y - 10   =  80  -10  =   70

Since x represent Brett age, then Brett's is 62 years old

Also, y represent Mark's age, therefore Mark is 80 years old

Finally z represent Carl's age, therefore Carl is 70 years old.

Answer:

12.

Step-by-step explanation:

The number of zeros to an equation is the highest power of the polynomial.

A quadratic equation whose highest degree is 2, has two solutions.

The equation f(x) = [tex]$ 3x^{12} - 17x^{8} + 11x^{4} - 6x + 23 $[/tex] will have 12 solutions (or zeroes) since the highest degree is 12.