Each ounce of Food I contains 3 g of carbohydrate and 2 g of protein, and each ounce of Food II contains 5 g of carbohydrate and 3 g of protein. Suppose x ounces of Food I are mixed with y ounces of Food II. The foods are combined to produce a blend that contains exactly 73 g of carbohydrate and 46 g of protein.
a. Explain why there are 3x + 5y g of carbohydrate in the blend and why we must have 3x + 5y = 73. Find a similar equation for protein. Sketch the graphs of both equations.
b. Where do the two graphs in part (a) intersect? Interpret the significance of this point of intersection

Answer:

3m ≤ ∫ f(x) dx ≤ 3M, at limit of b, a

Step-by-step explanation:

Like the question asked, which property of integral was used.

Property 8 of integrals was the basis upon which the question was solved.

The property of the integral is used to solve the problem. The function is given below.

[tex]3m & \leq \int_a^b f(x)dx \leq 3M \end{aligned}[/tex]

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

Suppose f has absolute minimum value m and absolute maximum value M.

We know that the property of the integral can be used.

If m ≤ f(x) ≤ M ∀ a ≤ x ≤ b. Then we have

[tex]m (b-a) \leq \int_a^b f(x) dx \leq M(b-a)\\[/tex]

Then we have

[tex]m \leq f(x) \leq M \ \ and \ \ 4 \leq x \leq 7[/tex]

This means that

[tex]\begin{aligned} m(7-4) & \leq \int_a^b f(x)dx \leq M(7-4)\\\\3m & \leq \int_a^b f(x)dx \leq 3M \end{aligned}[/tex]

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Answer:

4

Step-by-step explanation:

Answer:

Seth

Step-by-step explanation:

3/12 = 0.25

0.25*100 = 25%

Seth scored at 25%

2/10 = 0.2

0.2*100 = 0.2

0.2*100 = 20%

Zak scored at 20%

then:

25>20

then:

Seth scored on a greater fraction of his shots.

Zak scored on a greater fraction of his shots.

Given,

In a hockey game, Seth took 12 shots and scored 3 times.

Zak took 10 shots and scored twice.

We need to find who scored on a greater fraction of his shots.

We can compare fractions by finding their decimal values a nd comparing them.

Example: 1/2 and 2/5

1/2 = 0.5

2/5 = 0.4

0.5 is greater than 0.4.

Find the number of score Seth shots out of 12 shots.

= 3

We can write in fractions as:

3/12 _____(1)

Find the number of score Zak shots out of 10 shots.

= 2 x 3

= 6

We can write in fractions as:

6/10 _____(2)

Compare (1) and (2)

3/12 = 1/4 = 0.25
6/10 = 3/5 = 0.6

0.25 is less than 0.6

6/10 is a greater fraction than 3/12

Thus Zak scored on a greater fraction of his shots.

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Answer:

a.  y= e raise to power y

c. y = e^ky

Step-by-step explanation:

The first derivative is obtained by making the exponent the coefficient and decreasing the exponent by 1 . In simple form the first derivative of

x³ would be 2x³-² or 2x².

But when we take the first derivative of  y= e raise to power y

we get y= e raise to power y. This is because the derivative of e raise to power is equal to e raise to power y.

On simplification

y= e^y

Applying ln to both sides

lny= ln (e^y)

lny= 1

Now we can apply chain rule to solve ln of y

lny = 1

1/y y~= 1

y`= y

therefore

derivative of e^y = e^y

The chain rule states that when we have a function having one variable and one exponent then we first take the derivative w.r.t to the exponent and then with respect to the function.

Similarly when we take the first derivative of  y= e raise to power ky

we get y=k multiplied with e raise to power ky. This is because the derivative of e raise to a  constant and power is equal to constant multiplied  with e raise to power y.

On simplification

y= k e^ky

Applying ln to both sides

lny=k ln (e^y)

lny=ln k

Now we can apply chain rule to solve ln of y ( ln of constant would give a constant)

lny = ln k

1/y y~= k

y`=k y

therefore

derivative of e^ky = ke^ky

Answer:

12, 12 and 12 so 36

Step-by-step explanation:

Answer:

Step-by-step explanation:

5. (6.5 - 2)/(7 - 4) = 4.5/3 = 1.5

6. (8 - 8)/(-5 - 10)= 0/-15= 0

7. (-3 + .75)/(4 - 1) = -2.25/3 = -.75= -3/4

8. (2 + 7)/(18 - 18)= 9/0 = undefined

Answer:

Coordinates of the point B will be (14, 3.5).

Step-by-step explanation:

From the graph attached,

Distance between the Quarterback and Receiver = x-coordinate of the point B = 14 yards

Similarly, height of the football from the ground at point B = y-coordinate of the point B = 9 + [tex]\frac{12-9}{2}[/tex]

                   = 9 + 1.5

                   = 10.5 feet

Since, 1 feet = [tex]\frac{1}{3}[/tex] yards

10.5 feet = [tex]\frac{10.5}{3}[/tex]

               = 3.5 yards

Therefore, coordinates of the point B will be (14, 3.5).

Answer:

[tex] \sqrt{2 \times 2 \times 2 \times 3 } = \sqrt{24} = \sqrt{4 \times 6} = 2 \sqrt{6} [/tex]

Answer:

Step-by-step explanation:

w²+7w>293 is the inequality which we use to determine what lengths would make the area of the base of the tree house greater than 293 square Inches

The area of Rectangle is length times of width.

Given that Adam built a tree house with a rectangular base.

The length of the base is 7 inches more than its width.

Length=W+7

W is the width

The area of the base of the tree house greater than 293

We need to find the inequality to represent the area of the base of tree

Area of rectangle=Length×width

293=(w+7)w

293=w²+7w

As area is greater we have

w²+7w>293

Hence, w²+7w>293 is the inequality which we use to determine what lengths would make the area of the base of the tree house greater than 293 square Inches

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Answer:

7 and 9

Step-by-step explanation:

So we want two consecutive odd numbers whose product is 63.

Let's write an equation.

Let's let n be a random integer: doesn't matter what it is. Therefore, the first integer must be 2n+1.

This is because we're letting n be whatever it wants to be. If we multiply that whatever number by 2, then it will turn even. If we add 1 to an even number, it becomes odd.

Therefore, our first odd number is (2n+1). Our second, then, must be (2n+3).

Multiply them together. They equal 63. Thus:

[tex](2n+1)(2n+3)=63[/tex]

Expand:

[tex]4n^2+6n+2n+3=63[/tex]

Combine like terms:

[tex]4n^2+8n+3=63[/tex]

Subtract 63 from both sides:

[tex]4n^2+8n-60=0[/tex]

Divide both sides by 4:

[tex]n^2+2n-15=0[/tex]

And now, factor:

[tex](n+5)(n-3)=0[/tex]

Zero Product Property:

[tex]n+5=0\text{ or } x-3=0[/tex]

Find n:

[tex]n=-5\text{ or } n=3[/tex]

So, we've found n.

Then the first integer is either:

[tex]2(-5)+1 \text{ or } 2(3)+1[/tex]

Evaluate:

[tex]-9 \text{ or } 7[/tex]

However, we want two consecutive odd natural numbers. So, ignore the -9.

Therefore, our first odd integer is 7.

And our second one would be 9.

So, our answer is 7 and 9.

And we're done!

Answer:

Here are the basic steps to follow to simplify an algebraic expression:

remove parentheses by multiplying factors.

use exponent rules to remove parentheses in terms with exponents.

combine like terms by adding coefficients.

combine the constants.

Step-by-step explanation:

Answer:

Yes, provided they are all the same size.

Step-by-step explanation:

4/5=0.8

1/2=0.5

3/4=0.75

0.8+0.5+0.75=n

8+5=13

0.8+0.5=1.3

1.3+0.75=2.05

step 1: open up the brackets ( rmb to flip the signs )

step 2: bring 'a' to one side and the numbers to the other

6a + 34 = -3(-2a + 8)

6a + 34 = 6a - 24

6a - 6a = -24 - 34

0 = - 58

the final ans is kind of weird but here's my solution :))

Answer:

your pics a little blurry but if i am reading it right

the first one

f(x)=log x+5

1/8 since 4*2=8 and there is one spot you can land on with 6.

Answer:

2/8

Step-by-step explanation:

If you are spinning it twice and there is 4 places that is where you get the 8        The 2 comes from how many times you are spinning

18m

Step-by-step explanation:

5x3=15 +3 =18

Answer:

Option C

Step-by-step explanation:

It will be graphed as function:

Since is has a very small slope of 0.019 it will be shown almost parallel to x axis.

Some points on the graph:

Correct graph is option C

Answer: Area of Polygon Q is  [tex]\dfrac14[/tex]  of  Area of Polygon

Step-by-step explanation:

Given: Polygon Q is a scaled copy of Polygon P using a scale factor of [tex]\dfrac12[/tex] .

According to the property of scale factor ,

Area of the image = (scale factor )²x (Area of the original figure)

So, Area of Polygon Q = [tex](\dfrac12)^2[/tex]  x (Area of Polygon P)

⇒ Area of Polygon Q = [tex]\dfrac14[/tex]  x (Area of Polygon P)

Hence,  Area of Polygon Q is   [tex]\dfrac14[/tex]  of  Area of Polygon P.

Answer:

1/4

I did on khan

Step-by-step explanation:

Answer:

AB = 4.5

Step-by-step explanation:

Distance between A(-1, 2) and B(1, -2):

[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Let,

[tex] A(-1, 2) = (x_1, y_1) [/tex]

[tex] B(1, -2) = (x_2, y_2) [/tex]

[tex] AB = \sqrt{(1 - (-1))^2 + (-2 - 2)^2} [/tex]

[tex] AB = \sqrt{(2)^2 + (-4)^2} [/tex]

[tex] AB = \sqrt{4 + 16} = \sqrt{20} [/tex]

[tex] AB = 4.5 [/tex] (nearest tenth)

Answer:

(a) 0.16759

(b)  0.9649

Step-by-step explanation:

Given that:

n = 10 , p = 0.3 and  [tex]\hat p = 0.4[/tex]

[tex]P(|\hat p - p| > 0.2 ) = 1 - P ( |\hat p -p| \leq 0.2)[/tex]

= [tex]1 - P(-0.2 \leq \hat p-p \leq 0.2)[/tex]

= [tex]1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{\dfrac{pq}{n}}} \leq \dfrac{\hat p -p}{\sqrt{\dfrac{pq}{n}}} \leq \dfrac{0.2}{\sqrt{\dfrac{pq}{n}}} \end {pmatrix}[/tex]

[tex]=1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{\dfrac{(0.3)(1-0.3)}{10}}} \leq Z \leq \dfrac{0.2}{\sqrt{\dfrac{(0.3)(1-0.3)}{10}}} \end {pmatrix}[/tex]

[tex]=1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{\dfrac{(0.3)(0.7)}{10}}} \leq Z \leq \dfrac{0.2}{\sqrt{\dfrac{(0.3)(0.7)}{10}}} \end {pmatrix}[/tex]

[tex]=1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{0.021}} \leq Z \leq \dfrac{0.2}{\sqrt{0.021}} \end {pmatrix}[/tex]

[tex]=1 - P \begin {pmatrix} -1.380 \leq Z \leq 1.380 \end {pmatrix}[/tex]

= 1 - P( Z ≤ 1.380) - P(-1.380)

= 1 - ( 0.91620 - 0.08379 )

= 1 - 0.83241

= 0.16759

b) when n = 400; p =0.3 , q = 1 - p = 1 - 0.3 = 0.7

[tex]P( |\hat p - p | > 0.001) = 1- P ( |\hat p - p | < 0.001 )[/tex]

[tex]= 1- P ( -0.001 < \hat p - p < 0.001 )[/tex]

[tex]= 1- P ( \dfrac{-0.001}{\sqrt{\dfrac{pq}{n}}} < \dfrac{ \hat p - p}{\dfrac{pq}{n}} < \dfrac{0.001}{\sqrt{\dfrac{pq}{n}}} )[/tex]

[tex]= 1- P ( \dfrac{-0.001}{\sqrt{\dfrac{0.3\times 0.7}{400}}} < Z < \dfrac{0.001}{\sqrt{\dfrac{0.3 \times 0.7}{400}}} )[/tex]

[tex]= 1- P ( \dfrac{-0.001}{\sqrt{5.25 \times 10^{-4}}} < Z < \dfrac{0.001}{\sqrt{5.25 \times 10^{-4}}} )[/tex]

[tex]= 1- P ( -0.0436< Z < 0.0436)[/tex]

= 1 - P ( Z < 0.0436) - P ( -0.0436)

= 1 - (0.5176 - 0.4825)

= 1 -  0.0351

= 0.9649

ans is 25

Step-by-step explanation:

12(10-5)-40+(4+1)

=12 of 5 - 40 + 5

= 60 - 40 +5

=60 +5 - 40

=65-40

=25

Answer:

-25

Step-by-step explanation:

We start off by using PEMDAS. 10-5 then 4+1.

12(5)-40+5

we multiply, then add and subtract giving us -25

Answer:

i'm not sure so i'm sorry if it is not the right answer

Step-by-step explanation:

Let's assume AC is a straight line and B is on the line between A and C

AC=AB+BC

AC=4x+7+5x-8

AC=9x-1

Answer:

300 feet an hour

Step-by-step explanation:

in three hours they went down 1200 feet so that means in 1 hour they will go down 300 feet if they take no break

Answer:

The 10-yard line on a football field

Step-by-step explanation:

A geometric line segment is a straight path of points(that is a line) that has two end points (that is a beginning and an end). A 10 yard line on a football field is a line segment because it has two endpoints which is at the beginning of the 10 yard and at the end of the 10 yard.

A scientist's line of vision as he looks into space with a telescope is not a line segment because it extends forever (has no end).

A line of 15 dancers on stage is not a line segment, A light shone into the darkness is not a line segment because it continues forever and also, the hands of a clock is also not a line segment.

Answer:

Step-by-step explanation:

Answer:

1) 19.0km

2) 23.9mi

3) 53.9yd

4) 30.0mi

(all answers rounded off to the nearest tenth)

Step-by-step explanation:

Please see the attached pictures for full solution.