A researcher performs an experiment to test a hypothesis that involves the nutrients niacin and retinol. She feeds one group of laboratory rats a daily diet of precisely 41.59 units of niacin and 17,995 units of retinol. She uses two types of commercial pellet foods. Food A contains 0.22 unit of niacin and 100 units of retinol per gram. Food B contains 0.23 unit of niacin and 65 units of retinol per gram. How many grams of each food does she feed this group of rats each day

Answer:

y = 4x + 3

Step-by-step explanation:

If he has x seed packets, Johnny can grow 4 * x = 4x plants. The 3 is a constant because he already has 3 so the equation is y = 4x + 3.

Answer:  The difference is approximately $44. Remember that is not an exact amount because the weeks are approximated and the second offer was also approximated.

Step-by-step explanation:

If one has $61,100 and the other has 63,400 annually which means that is the amount they will be offered a year. So first we need to determine how many weeks are in a year.There are approximately 52 weeks in one year so we will divide the salaries by 52 to find how much they each offer in one week.

First Offer:  61,100 / 52 =  1175  

Second Offer:  63,400/52=  approximately 1219    

Now find the difference between the numbers

1219. - 1175 =  $44

The difference in weekly pay for these two job will be around $0.04k.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Number of weeks in 1 year = number of weeks in 1 month × 12

Number of weeks in 1 year = 4 × 12 = 48

Annual salary in the first job = $61.1k

So weekly salary of first job =$1.28k

Annual salary in the second job = $63.4k

So weekly salary of second job = $1.32k per week

Difference between weekly pay = 1.32 - 1.28 = 0.04k

Hence "The difference in weekly pay for these two job will be around $0.04k".

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Answer:

Please see attached picture

hope it helped you:)

Answer:8,2,0,2,8; Graph A

Step-by-step explanation:

The graph of the given equation best represents a parabola.

A graph represents the nature of the equation graphically by plotting the points of it.

Given, y = 2x²

For x = - 2, y = 2(- 2)² = 8

For x = - 1, y = 2(- 1)² = 2

For x = 0, y = 2(0)² = 0

For x = 1, y = 2(1)² = 2

For x = 2, y = 2(2)² = 8

Therefore, the given table will be:

x  - 2   - 1   0   1   2

y    8     2   0  2   8

By plotting the graph, it is clear that, the graph best represents a parabola.

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Answer:

1/6

Step-by-step explanation:

For a set of vectors a, b and c to be linearly dependent, the linear combination of the set of vectors must be zero.

C1a + C2b + C3c = 0

From the question, we are given the set S={u−3v,v−2w,w−ku}, the corresponding vectors are a(0, -3, 1), b(-2,1,0) and c(1,0,-k)

The values in parenthesis are the ccoefficients of w, v and u respectively.

On writing this vector as a linear combination, we will have;

C1(0, -3, 1) + C2(-2,1,0) + C3(1,0,-k) = (0,0,0)

0-2C2+C3 = 0........ 1

-3C1+C2 = 0 ........... 2

C1-kC3 = 0 ….......... 3

From equation 2, 3C1 = C2

Substituting into 1, -2(3C1)+C3 = 0

-6C1+C3 = 0

-6C1 = -C3

6C1 = C3.…..4

Substitute 4 into 3 to have

C1-k(6C1) = 0

C1 = k6C1

6k = 1

k = 1/6

Hence the value of k for the set of vectors to be linearly dependent is 1/6

Answer:

Step-by-step explanation:

1. binomial polynomial

2. 2 terms

3. 4 is the constant term

4. - 1/10 x^3 is the leading term

5. -1/10 is the leading coefficient.

Answer:

Length= 30 ft

Width= 18ft

Step-by-step explanation:

The perimeter of the rectangular patio is to be 96 feet.

the length is to be 6 feet less than twice the width

Perimeter=2(length+width)

But

Length= 2(width)-6

Substituting in perimeter equation

Perimeter=2(length+width)

Perimeter=2((2(width)-6)+width)

Perimeter= 96 feet

Let width= x

Perimeter=2((2(width)-6)+width

96=2((2(x)-6)+x)

96= 4x-12+2x

108= 6x

18= x

Width= 18ft

Length= 2(width)-6

Length= 2(18)-6

Length= 36-6

Length= 30 ft

Answer: 62°

Step-by-step explanation:

apply concept: the interior angle sum of triangle is = 180°

          a+b+c=180

a+68.5+49.5=180

            a+118=180

                  a=62

Answer:

Step-by-step explanation:

Since it's a triangle it's interior angles sum up to 180° .

In order to find x add up all it's known interior angles and subtract it from 180° to find x.

That's

x + 68.5 + 49.5 = 180

x + 118 = 180

x = 180 - 118

We have the final answer as

Hope this helps you

Answer:

0 belongs to the set of whole number,set of rational numbers,set of real numbers and integers

Step-by-step explanation:

Answer:

X=2

Step-by-step explanation:

First, distribute the 3 to get

3x+3-2=x+5

Solve for 3-2 to get

3x+1=x+5

subtract 1 from both sides to get

3x=x+4

subtract x from both sides to get

2x=4

divide both sides by 2 to finalily get

x=2

Answer:

5

Step-by-step explanation:

The leading coefficient is the coefficient with a variable with the greatest exponent.The exponent is the number you would say "the power to". What I mean is let's say you have this number: [tex]3^{2}[/tex] . The exponent would be 2 in this equation because it's saying what power 3 is too. Therefore, 5 is the leading coefficient.

Answer:

= 274

Step-by-step explanation:

202 + 6(9 + 3)

= 202 + 9 * 12

= 202 + 72

= 274

Answer:

Its is actually 472

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\rho=1.6125\dfrac{g}{cm^3}}[/tex]

Step-by-step explanation:

The formula of a density:

[tex]\text{density}=\dfrac{mass}{volume}\Rightarrow\rho=\dfrac{m}{V}[/tex]

We have

[tex]\text{mass}\ m=12.9g\\\\\text{volume}\ V=8cm^3[/tex]

Substitute:

[tex]\rho=\dfrac{12.9g}{8cm^3}=\dfrac{12.9\cdot10}{8\cdot10}\dfrac{g}{cm^3}=\dfrac{129}{80}\dfrac{g}{cm^3}=1.6125\dfrac{g}{cm^3}[/tex]

The the density of the brown sugar is equal to [tex]1.6125 \;g/cm^3[/tex]

Given the following data:

To find the density of the brown sugar;

Density can be defined as mass all over the volume of an object.

Simply stated, density is mass per unit volume of an object.

Mathematically, the density of a substance is given by the formula;

[tex]Density = \frac{Mass}{Volume}[/tex]

Substituting the values into the formula, we have;

[tex]Density = \frac{12.9}{8}[/tex]

Density =  [tex]1.6125 \;g/cm^3[/tex]

Therefore, the the density of the brown sugar is equal to [tex]1.6125 \;g/cm^3[/tex]

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Answer:

6.25

Step-by-step explanation:

The perimeter is the sum of the lengths of the sides.

For a rectangle, it's the two widths plus the two heights.

P = 2W + 2H

Plugging in values:

52 = 2(3x − 1) + 2(x + 2)

52 = 6x − 2 + 2x + 4

52 = 8x + 2

50 = 8x

x = 6.25

Find the value of x.

Perimeter of rectangle = 2 ( l + b )

We know that,

Perimeter of rectangle = 52 [ Given ]

⇒ 2 ( l + b ) = 52

⇒ 2 ( 3x - 1 + x + 2 ) = 52

⇒ 2 ( 4x + 1 ) = 52

⇒ 8x + 2 = 52

⇒8x = 52 - 2

⇒ 8x = 50

⇒ x = 50/8

⇒ x = 6.25 inches

Answer:

the answer is 8. just think of it as subtraction. subtract +6 from +14. then you get the answer for +14+-6.

Answer:

C

Step-by-step explanation:

Here we have the question,

7x+4 = -19 + 5x

Now we add 19 to both sides,

7x + 4 + 19 = -19 + 19 + 5x

7x + 23 = 5x

Now we subtract 7x from both sides,

23 = -2x

We divide -2 from both sides,

x = -23/2

Now we plug this in into 2x - 14,

2(-23/2) - 14 = -23-14 = -37

Our answer is C

Answer:

y2=16-x

x=0

y2=16-0

y2=16

y2/2=16/2

y=8

Answer: 3 people ordered soup.

Step-by-step explanation:

Let x be the number of people ordered salad and y  be the number of people ordered soup.

As per given,

x=2y           (i)

7.50x+6.25y= 63.75          (ii)

Substitute value of c =2y in (ii) , we get

7.50(2y)+6.25y= 63.75

⇒ 15y+6.25y =  63.75

⇒21.25y =  63.75

⇒ y= 3   [divide both sides by 21.25]

Then, x= 2(3) =6

So 6 people ordered salad and 3 people ordered soup.

Answer:

Standard form:

Simplify the words.

6,090,036

Expanded form:

Take the standard number and expand it.

6000000 + 90000 + 30 + 6

I'm sorry if I misunderstood.

Good luck though! :)

Please add Brainliest if you'd like, not that it matters.

Answer:

y= -7

Step-by-step explanation:

This line is a horizontal line.

Horizontal lines all have the same form of y=k (where k is the y-intercept of the horizontal line).

The y-intercept is the point where the line meets the y-axis (the vertical axis). For this line, the y-intercept is in between -6 and -8, making it: (0,-7) or just -7.

Let's return to the form for horizontal lines.

y= k

The y-intercept is -7. Substitute -7 in for k.

y= -7

The equation of the line is y= -7

Step-by-step explanation:

(2) (x+2)^2 + (-15x -3)

I hope this will be helpful for you.

Answer:

[tex]2(x + 2)^{2} + (-15x - 3)[/tex]

The guy above is correct

Proof :

[tex]2(x + 2)^{2} - 15x - 3 \\ 2((x + 2)(x + 2) - 15x - 3 \\ 2( {x}^{2} + 4x + 4) - 15x - 3[/tex]

[tex]2 {x}^{2} + 8x - 15x + 8 - 3 \\ 2 {x}^{2} - 7x + 5[/tex]

My workings are in the picture

My asnwer was 5/2 and -1

As we know that 1 mile=1.6km

then,

62 miles=62*1.6km

=99.2km/hour

so, yes we are driving under the speed limit.

Answer:

Yes

Step-by-step explanation:

Convert 62 mph to kph by multiplying it by 1.6

62(1.6)

= 99.2

Yes, you are driving under the speed limit

Answer:

119.45 m

Step-by-step explanation:

Given:

When angle of elevation of the sun changes from 58° to 36° the length of shadow of a pole increases by 90 m.

To find:

Length of pole = ?

Solution:

Kindly refer to the attached image.

[tex]\triangle ABC[/tex] represents the 1st angle of elevation of sun i.e.  58°

[tex]\triangle ABD[/tex] represents the 2nd angle of elevation of sun i.e.  36°

Change in shadow is represented by CD = 90 m

Let height of pole, AB = [tex]h[/tex] m

Let side BC = [tex]x[/tex] m

Now, let us apply tangent rules in [tex]\triangle ABC, \triangle ABD[/tex] one by one:

[tex]tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan58^\circ=\dfrac{AB}{BC}\\\Rightarrow tan58^\circ=\dfrac{h}{x}\\\Rightarrow x = 0.624h ..... (1)[/tex]

[tex]tan36^\circ = \dfrac{h}{x+90}[/tex]

Putting value of [tex]x[/tex] using equation (1):

[tex]tan36^\circ = \dfrac{h}{0.624h+90}\\\Rightarrow 0.726\times 0.624h+0.726\times 90 = h\\\Rightarrow h-0.453h =65.34\\\Rightarrow \bold{h = 119.45\ m}[/tex]

119.45 m is the height of pole.

Answer:

Total number of votes- 145,000

Votes secured by winning candidate- 76,850

Step-by-step explanation:

Candidate A- 47%

Candidate B- 53%

6% difference or 8700 votes so

6%=8700

1%=1450

100%=145,000

53%= 76,850

Answer:

1

Step-by-step explanation:

Answer:

x-3

Step-by-step explanation:

x²-9÷x+3=x-3

Answer:

3

Step-by-step explanation:

because it's being intersected

hope I helped?

Answer:

RK= 13      SK= 12

Step-by-step explanation

First, we find the missing length of RK using the given information: 65-52=13

Then we divide 65 by 13 to get a scale factor: 65/13=5

(To check, we multipuly: 13*5=65)

We then apply the scale factor to MK to find SK: 60/5=12

(To check we multipuly: 5*12=60)

We now have our answers: RK:13, SK:12

Answer:

Hey there!

The correct answer would be a line from (0, 0) to (-1, 2)

Let me know if this helps :)

Answer:

0.00387

To convert from meters to kilometers, you must divide the number pf meters by 1000.

3.87 ÷ 1000 = 0.00387.

So, that is the answer. Hope it helps!