As a clinical trials monitor, you recruit subjects for a new study. You want 175 subjects per group for 3 groups. How many subjects should you recruit for the whole study?

The two angles are corresponding angles, so they are congruent (due to the horizontal lines being parallel)

x+15 = 102

x+15-15 = 102-15 .... subtract 15 from both sides

x = 87

Answer:

y-12= -3(x-6) (point slope form)

y = -3x + 30  ( slope intercept form)

Initial delivery time = 30 minutes

delivery time decreases 3 minutes per day

Step-by-step explanation:

To find equation of line we pick two points from the graph

(3,21)  and (6,12)

Point slope form of a line is y-y1= m(x-x1)

m is the slope and (x1,y1) is the point on graph

Lets find out slope m

[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{12-21}{6-3} =-3[/tex]

(x1,y1) is (6,12)

Point slope form of a line is y-y1= m(x-x1)

y-12= -3(x-6) (point slope form)

Now we solve for y to get slope intercept form

y-12 = -3x +18

Add 12 on both sides

y = -3x + 30  ( slope intercept form)

(b) To find initial time we plug in 0 for x

y = -3x + 30

y= -3(0) + 30

y=30

Initial delivery time = 30 minutes

Slope is the delivery time decreases per day

We got slope m = -3

So delivery time decreases 3 minutes per day

Answer:

well basically  y-12= -3(x-6) (point slope form)

y = -3x + 30  ( slope intercept form)

Initial delivery time = 30 minutes

delivery time decreases 3 minutes per day

Step-by-step explanation:

To find equation of line we pick two points from the graph

(3,21)  and (6,12)

Point slope form of a line is y-y1= m(x-x1)

m is the slope and (x1,y1) is the point on graph

Lets find out slope m

(x1,y1) is (6,12)

Point slope form of a line is y-y1= m(x-x1)

y-12= -3(x-6) (point slope form)

Now we solve for y to get slope intercept form

y-12 = -3x +18

Add 12 on both sides

y = -3x + 30  ( slope intercept form)

(b) To find initial time we plug in 0 for x

y = -3x + 30

y= -3(0) + 30

y=30

Initial delivery time = 30 minutes

Slope is the delivery time decreases per day

We got slope m = -3

So now we can say that the delivery time decreases 3 minutes per day! Hope this helps :)

Step-by-step explanation:

Answer:

[tex]\frac{(L x M)}{6}[/tex]

Step-by-step explanation:

The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.

The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.

We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.

As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.

We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.

[tex]\frac{(L x M)}{6}[/tex]

Answer:

yes

6r=18

Step-by-step explanation:

To solve this problem, plug 8250 in for b and 15 in for t and then solve for k:

[tex]8250=1000e^{15k}[/tex]

*Divide both sides by 1000*

[tex]8.25=e^{15k}[/tex]

*Take the natural log (ln) of both sides*

2.1102=15k

*Divide both sides by 15*

0.1406=k

0.1406 rounds to 0.141 which is close to a. 0.143.

Hope this helps!!

Answer:

A Jones has the best plus minus record

Step-by-step explanation:

The player wants the most "negative" score, which means he was one the ice when his team scored the most points and off the ice when his team was scored upon.

Answer:

11. a. See below. b. E. Simpson

Step-by-step explanation:

11. a. Graphing on the number line

You did a great job on this.

I just used red dots to make them more visible.

===============

11. b. Best plus-minus record

The player with the best plus-minus record is E. Simpson.  

His plus-minus record of +9 means that his team has scored more often when he is on the ice than any other player.

Final answer:

There are 1,320 possible ways to distribute the gold, silver, and bronze medals among twelve athletes with no ties.

Explanation:

The student has asked how many possible ways three medals can be distributed among twelve athletes, assuming there are no ties. This can be calculated using permutations since the order of medals (gold, silver, bronze) matters and each medal can only be given once.

For the gold medal, there are 12 potential athletes, for the silver there are 11 remaining athletes (since one has already received gold), and for the bronze, there are 10 athletes left. Therefore, the number of possible ways to distribute the three medals is:

12 (options for gold) × 11 (options for silver) × 10 (options for bronze) = 1,320 possible ways.

Answer: x^3y^4 is the lowest common denominator.

Step-by-step explanation: To get both expressions to have a common denominator, multiply both of them to get them equal. For the first expression, multiply the numerator and denominator by y^3: 3y^3/x^3y^4

The second expression should be multiplied by the numerator and denominator by x^2: 7x^2/x^3y^4

(Add exponents when multiplying them) Now both expressions have common denominators.

Answer:

x^3*y^4

Step-by-step explanation:

The two denominators shown are x^3*y and x*y^4.  The LCD must involve the largest power of x, which is x^3, and the largest power of y, which is y^4.  Thus, the LCD is x^3*y^4.

the value of the expression is approximately - 25.4349.

To find the value of the expression (- 3)³ + 6⁽³/¹²⁾, we follow the order of operations. First, we evaluate the exponentiation:

(- 3)³ = (- 3) × (- 3) × (- 3) = -27

Next, we simplify the second term:

6⁽³/¹²⁾ = 6⁽¹/⁴⁾ = √( √6) ≈ 1.5651

Finally, we add the two results:

(- 3)³ + 6⁽³/¹²⁾ = - 27 + 1.5651 ≈ - 25.4349

So, the value of the expression is approximately - 25.4349. The explanation highlights the steps of evaluating the exponentiation and simplifying the second term before performing the addition to get the final result.

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Answer:

The company should charge $ 3.25 for the smaller size.

Step-by-step explanation:

The price per ounce of the 32-ounce product is required to be 25% greater than the larger-sized product.

We know that for the size of 48 ounces the price is $ 3.90

So, the price per ounce is:

[tex]\frac{3.90}{48}[/tex]= $ 0.08125

For the smallest size the price per ounce should be 25% higher.

So:

$ 0.08125 (1 + 0.25) = $ 0.10156

The total price for the smallest size is:

$ 0.10156 * 32 = $ 3.25

The company should charge $ 3.25 for the smaller size.

Answer:

3.25

Step-by-step explanation:

We could solve this problem by figuring out the per-ounce cost of the 48-ounce package, increasing it by $25\%$, and then multiplying that by 32 for the smaller package. However, if we simply increase the price by $25\%$, and then scale the package size down to 32 ounces from 48 ounces, these are the same calculations, but in a different order that makes it easier to calculate. Thus: $3.90 \times 1.25 \times \frac{32}{48} = \boxed{3.25\text{ dollars}}$

The surface area of the cylinder is approximately 191.9 square inches.

The surface area of a cylinder is the sum of the areas of its curved surface and its two circular bases. The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

where SA is the surface area, r is the radius of the circular base, h is the height of the cylinder, and π is the mathematical constant pi (approximately equal to 3.14159).

The first term on the right-hand side of the equation (2πr²) represents the area of the two circular bases of the cylinder. The second term (2πrh) represents the area of the curved surface of the cylinder.

The area of the square embedded in the circular base of the cylinder is 18 in², which means each side of the square has a length of √18 in = 3√2 in. Since the square is embedded in the circular base, the diameter of the base of the cylinder is equal to the diagonal of the square, which is 2 times the length of one side, or 6√2 in.

The radius of the circular base is half the diameter, or 3√2 in. The surface area of the cylinder consists of the area of the top circular base, the area of the bottom circular base, and the lateral area (the curved surface area) of the cylinder.

The area of each circular base is πr² = π(3√2)² = 18π in².

The lateral area of the cylinder can be found by multiplying the height (which is given as 10 inches) by the perimeter of the circular base (which is 2πr). The perimeter of the circular base is 2π(3√2) = 6π√2 in. Therefore, the lateral area is 10(6π√2) = 60π√2 in².

The total surface area of the cylinder is the sum of the areas of the two circular bases and the lateral area:

Surface area = 2(18π) + 60π√2

= 36π + 60π√2

≈ 191.9 in² (rounded to one decimal place)

Therefore, the surface area of the cylinder is approximately 191.9 square inches.

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The solution is: Area of actual Patio is:  170 ft²

Given:

Patio drawing of 4.25 in by 2.5 in

Scale of Patio to its drawing = 4ft to 1 in

Requires:

Area of actual Patio

SOLUTION:

Area of actual Patio = area of a rectangle = length × width

Given a scale drawing of 4ft to 1 in, therefore:

Length of actual Patio = 4.25 × 4 = 17 ft

Width of actual Patio = 2.5 × 4 = 10 ft

Therefore:

Area of actual Patio = 17 ft × 10 ft = 170 ft²

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complete question:

A contractor is given a scale drawing of a rectangular patio. The scale from the patio to the drawing is 4ft to 1in. What is the area of the actual patio?

[tex]\dfrac{p+3}{p^2+7p+10}=\dfrac{p+3}{p^2+5p+2p+10}=\dfrac{p+3}{p(p+5)+2(p+5)}=\dfrac{p+3}{(p+2)(p+5)}\\\\\dfrac{p+5}{p^2+5p+6}=\dfrac{p+5}{p^2+3p+2p+6}=\dfrac{p+5}{p(p+3)+2(p+3)}=\dfrac{p+5}{(p+3)(p+2)}\\\\\text{Lowest Common Denominator of}\ \dfrac{p+3}{p^2+7p+10}\ \text{and}\ \dfrac{p+5}{p^2+5p+6}\\\\\text{is}\ (p+5)(p+2)(p+3)\to\boxed{A.}[/tex]

Answer:

1/3 is your answer

Step-by-step explanation:

Note that in the slope intercept form, the equation looks like: y = mx + b

Isolate the y. First, subtract 3x from both sides

3x (-3x) - 9y = (-3x) + 4

-9y = -3x + 4

Next, to fully isolate the y, divide - 9 from both siedes

(-9y)/(-9) = (-3x + 4)/(-9)

y = (-3x + 4)/-9

Simplify

y = (1/3)x - 4/9

You're slope of the line (m in y = mx + b) is 1/3

~

Hey there, we are given quite a lot of information in this problem. First of all, let's make an equation.

y = x - 22

where y = student's age

where x = instructor's age

this equation is correct because x(instructor) - 22 will yield the student's age (y).

If the instructor were 44 years old, the student would be 22 years old.

y = 44 - 22

y = 22

If the instructor were 66 years old, the student would be 44 years old.

y = 66 - 22

y = 44

To find the length of the wall represented by a line that is 3 7/8 inches long on the blueprint, we can use the scale conversion. The length of the wall is 15 1/2 feet.

To find the length of the wall represented by a line that is 3 7/8 inches long on the blueprint, we need to use the scale conversion.

The given scale is 1 inch corresponds to 4 feet.

So, we can set up a proportion:

1 inch − 4 feet

3 7/8 inches − x feet

To solve for x, we can cross-multiply:

1 × x = 4 × 3 7/8

Multiply 4 by the whole number 3 and then add the product to the result of 4 multiplied by the fractional part 7/8.

x = 12 + 28/8

x = 12 + 3 1/2

x = 15 1/2 feet

Therefore, the length of the wall represented by a line that is 3 7/8 inches long on the blueprint is 15 1/2 feet.

When an exponent is negative, you move it to the other side of the fraction to make the exponent positive.

For example:

[tex]x^{-2}[/tex] or [tex]\frac{x^{-2}}{1} =\frac{1}{x^2}[/tex]

[tex]\frac{1}{y^{-3}} =\frac{y^3}{1}[/tex] or y³

f(-2) This means that x is -2, so you can plug in -2 for "x" in the equation

[tex]f(x)=3^x[/tex]

[tex]f(-2)=3^{-2}[/tex]

[tex]f(-2)=\frac{1}{3^2}[/tex]

[tex]f(-2)=\frac{1}{9}[/tex]

Your answer is D

The value of the function f(-2) will be 1/9

A mathematical relationship from a set of inputs to a set of outputs is called a function.

The given function is f(x) = [tex]3^{x}[/tex]

∴ f(-2) will be = [tex]3^{-2}[/tex]

So,  [tex]3^{-2}[/tex] will be equal to 1/9

∴ The value of f(-2) will be 1/9

Option D is correct.

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Answer:

The answer c

Hope I helped :)

Step-by-step explanation:

Solve for x by simplifying both sides of the equation then isolating the variable.

Exact Form:

x=1/3

Decimal Form:

x=0.333333333

Answer:

b

Step-by-step explanation:

3.27 Times 10⁻⁴ in standard form is 0.000327. This is found by moving the decimal point in 3.27 four places to the left, resulting in the number 0.000327.

The number 3.27 TImes  10⁻⁴ into standard form.

To do this, we move the decimal point four places to the left, because the exponent on the 10 is negative four.

So, starting with the number 3.27, we move the decimal point to the left four times, which introduces three zeros after the decimal point and before the 327.

The correct answer is B: 0.000327.

This means that 3.27 times  10⁻⁴ is equivalent to 0.000327 when written in standard form.

Answer:

C is your answer

Step-by-step explanation:

Add every number by 14

Answer:

False

Step-by-step explanation:

(-2,0)  x is equal to -2 and y = 0

y=x  

Substitute the values in.

-2 =0

False

Answer: I believe the answer is C

Step-by-step explanation:

Answer:

19 minutes.

Step-by-step explanation:

55-36=19.

For this case we have to indicate how much time the brownies are needed to bake, knowing that 55 minutes are given and Teresa reviewed them after 36 minutes.

For this we subtract:

[tex]55 \ minutes-36 \ minutes = 19 \ minutes[/tex]

So brownies have 19 minutes to bake

Answer:

19 minutes

Answer: 8?

Step-by-step explanation:

Answer:

slope = - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = - 2x is in this form

with slope m = - 2 and c = 0

So for this, we will be setting up a system of equations with the information we have:

[tex]x+y=13\ \textsf{"The sum of two numbers is 13."}\\2x-3y=1\ \textsf{"Two times the first number minus three times the second number is 1."}[/tex]

Now we have our system of equations set up. Next, I will be using the substitution method to solve this system. So firstly, subtract y on both sides of the first equation:

[tex]x=13-y\\2x-3y=1[/tex]

Now, substitute x for (13 - y) in the second equation and solve for y as such:

[tex]2(13-y)-3y=1\\26-2y-3y=1\\26-5y=1\\-5y=-25\\y=5[/tex]

Now that we have the value of y, substitute it into either equation to solve for x:

[tex]x+5=13\\x=8\\\\2x-3(5)=1\\2x-15=1\\2x=16\\x=8[/tex]

In short, the first number (x) is 8 and the second number (y) is 5.

Answer:

The answer is 198.

Step-by-step explanation:

First you need to know how much is a batch of cookies which is 60. Since she made 3 batches that means you will need to multiply 3 by 60, which will give you 180 cookies. Next you will need to add 2 to 10 because thats how much were took. That equals 12. Subtract 12 from 180 and that will give you 168. Last but not least you will need to add 30 because that is half the batch of cookies her neighbor gave to her. So 168 plus 30 equals 198.

Answer:

198

Step-by-step explanation:

source = trust me bro