Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 4 ≤x≤ 8.

The oil he use  in the salad 291.66ml

What is Ratio ?

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

The formula below can be used to determine how much oil Jack consumes:

Jack uses x amount of mayonnaise to make y amount of salad dressing * (5 / (5 + 7)) ---. (1)

If we change the number of ml of salad dressing Jack prepares in equation (1), we get the following result:

Jack uses 291.66 ml of oil, which is equal to 700ml * (5/ (5 +7))

Hence, it will take 291.66ml of oil

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The algebraic expression for the cost of t T-shirts, not including sales tax is  15.95t - 5.

Given that:-

Cost of a T-shirt = $ 15.95

Discount on coupon = $ 5 (can be used for one T-shirt only)

We have to write an algebraic expression for the cost of t T-shirts, not including sales tax.

We know that,

Total cost of T-shirts = (Number of T-shirts)*(Cost of one t-shirt) - Discount

Hence, we can write,

C(t) = t*(15.95) - 5

C(t) = 15.95t - 5

Where, C(t) is the cost of t T-shirts and t is the number of T-shirts.

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Answer:

Step-by-step explanation:

0.000000005% can be written as a fraction: 0.000000005 / 100

Question 2a

[tex]x+6+x+3=17 \\ \\ 2x+9=17 \\ \\ 2x=8 \\ \\ x=4[/tex]

Question 3a

[tex]1+2x+31=x+20 \\ \\ 2x+32=x+20 \\ \\ x+32=20 \\ \\ x=-12[/tex]

Answer:

Box on the right is 6 and the lower box on the left is 840

Step-by-step explanation:

Make a proportion:

[tex]\frac{168}{1008}[/tex] =[tex]\frac{1}{x}[/tex]  cross multiply and solve

168x = 1008  Divide both sides by 168

x = 6

[tex]\frac{168}{x}[/tex] = [tex]\frac{1}{5}[/tex]  Cross multiply and solve

x = 168(5)

x = 840

Answer: Question E: The answer is that A(9) is greater.

Step-by-step explanation:

For questions A and C, you can see that the table is exponentially growing. So the equation will use multiplication. You can also see the value of the equation is growing by x2.

So you could say the table starts at a base of 1/2, then grows exponentially at a rate of 2. (Basically saying the value grows x2 per term). The equation will result in y= 1/2(2)^x

For questions B and D, you can see that the graph is growing linearly. So the equation will use multiplication.

By drawing a line between the lines you can easily see the growth of the triangle. You can then tell the 0th term to 1st term goes right 1 and up 10.

Next, you look at the 1st term to the 2nd term. You can tell that it goes right 1 and up 10. So, the rate is 10 per term. (10x) and it starts at 2 (+2). The equation will result in y=10x+2

Question E, solve each equation by substituting the x by 9.

A(9)

y= 1/2(2)^x

y= 1/2(2)^9

y= 1/2(512)

y=256

B(9)

y=10x+2

y= 10(9) +2

y= 90+2

y=92

The answer is that A(9) is greater.

the horizontal asymptote as x tends to infinity that is  approaches positive infinity of \sqrt{4x^2+ 9x} - \sqrt{4x^2 +x} is 2

What do the asymptotes mean?

Definition of asymptote

a straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the

slope of the line

[tex]f(x)=\sqrt{4x^2+9x}-\sqrt{4x^2+x} \\\\f(x)=2x(1+\frac{9}{4x}) ^{\frac{1}{2} } -2x(1+\frac{1}{4x})^\frac{1}{2}[/tex]

[tex]f(x)=2x( 1+\frac{1}{2} .\frac{9}{4x} +...... -1 -\frac{1}{2} .\frac{1}{4x} - ......)[/tex]

all the other terms involve 1/powers of x which vanish as x tends to infinity

[tex]f(x)=\frac{9}{4} -\frac{1}{4} +...[/tex]

Hence

[tex]\lim_{x \to \infty} f(x)=2[/tex]

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60 number of packages needed to have the same number of hamburgers and buns.

In this problem, we are using the concept of Least Common Multiple. The least common multiple (LCM) of two numberts is the smallest number that can be partitioned by both numbers. To have the same number of  buns and hamburgers, we just need to  calculate the least common multiple of 20 and 12

12's Multiples = 12, 24, 36, 48, 60, 72, 90

20's Multiples = 20, 40, 60, 80, 100

Here we can see the common multiple of 20 and 12 is 60, and the LCM of 20 and 12 is 60. Therefore they need to buy  60 packages in order to have the same number of hamburgers and buns

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Answer:

Answer is 1097.28 cm

Step-by-step explanation:

prove me wrong

Answer:

1097.28

Step-by-step explanation:

There are 91.44 centimeters per yard

12 x 91.44

The number of baby camels at the zoo is 44.

Given: The number of adult camels is 6 and the number of baby camels is 5 for every 6 camels respectively.

To find :We have to find how many baby camels are at the zoo.

Explanation:

Step 1:The ratio of adult camels and baby camels is 6:5

Step 2:Let the number of adult camels = 6x .

Step 3:Let the number of baby camels = 5x

Step 4:It is given that the total number of adult camels and baby camels is 44 at the zoo. So According to the questions,

⇒6x+5x=44

⇒11x=44

⇒x=44/11

⇒x=4

∴The number of adult camels = 6×4

                                               = 24

And the number of baby camels at the zoo.

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Answer:

  22 ft

Step-by-step explanation:

Given a river that has a depth in January of -5 ft, and a depth in July of -27 ft, you want the difference between the depths in January and July.

The difference between two numbers is found by subtracting the second from the first:

  (January depth) - (July depth) = (-5 ft) -(-27 ft)

  = (-5 +27) ft = 22 ft

The difference between depths in January and July is 22 feet.

The solution for the linear equation is:

a = 1/4.

I believe we have the linear equation:

(a + 2)/3 = 3/4

To solve this, we need to isolate the variable a in one of the sides of the linear equation, to do so, we can start by multiplying both sides by 3.

3*(a + 2)/3 = 3*(3/4)

a + 2= 9/4

Now we can subtract 2 in both sideS:

a + 2 - 2 = 9/4 - 2

a = 9/4 - 8/4 = 1/4

a = 1/4

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The inequality to find the scores she must make on the final exam to pass the course with an average of 77 or higher is (310 + x) / 5 >= 77.

The meaning is that she should have a score of 75 or higher to pass.

From the information, Shureka washburn has scores of 69,80,71, and 90 on her algebra tests and she must make on the final exam to pass the course with an average of 77 or higher.

Therefore, the inequality to express the information will be:

(69 + 80 + 71 + 90 + x)/5 >= 77

(310 + x) / 5 >= 77

Crops multiply

310 + x >= 77 × 5

310 + x >= 385

x >= 385 - 310

x >= 75

She needs 77 or more in order to pass the course.

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Answer:

Step-by-step explanation:

The maximum number of seats that might not be filled during her performance is 1738 , the the inequality representing this story is 4000+x≤5738 .

In the question ,

it is given that

Luisa Miller always brings crowds of at least 4,000 people, and

Sydney Opera House can house no more than 5738 people

no more than is represented by the inequality "≤" .

let x be the number of empty seats during her performance .

So, according to the question , the inequality becomes

4000+x≤5738

on solving further , we get

x ≤ 5738-4000

x ≤ 1738

So, maximum number of seats that might not be filled during her performance is 1738 .

When the inequality x ≤ 1738 , will be graphed then the limit will be an closed circle as equal to sign is included in the inequality .

as when the numbers decreases , it move towards left side

So, When the inequality is graphed, the line will have an arrow pointing towards the left .

Therefore , the maximum number of seats that might not be filled during her performance is 1738 ,

the the inequality representing this story is 4000+x ≤ 5738 ,

the limit of graph will be closed circle and arrow will be pointing towards left .

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If ratio of m to n is equal to 5 then, m = 5n

Ratios :- The quantitative relation between two amounts showing the number of times one value contains or is contained within the other are known as ratios.

m/n = 5

m = 5    

Therefore, option b is correct i.e. m = 5.                                    

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Answer:

area= l x b

area= (6-d)3

area= 18-3d

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True.

Given the statement 'If the distance from 0 to x on a number line is greater than 5, then -5+x is positive' is True.

For the given question,

The distance from 0 to x on a number line is greater than 5

We write the above statement in mathematical expression form as,

⇒ |x - 0| > 5

⇒ |x| > 5

⇒ x > 5  

We need to determine the value of an expression -5 + x

From (1),

⇒ x > 5  

Subtract -5 from both sides,

⇒ -5 + x = -5 + 5

⇒ -5 + x > 0

From the above expression, we observe that the value of the expression is always greater than 1.

This means the value of an expression -5 + x is positive.

Therefore, the given statement 'If the distance from 0 to x on a number line is greater than 5, then -5+x is positive' is True.

In mathematics, a number line can be described as a figure that symbolizes numbers on a consecutive line. The digits on a number line are positioned successively with equal spacing along its length. It can be infinitely expanded in any direction and is often depicted horizontally.

Absolute value is the distance between a digit and zero on a number line. Since the space is forever positive, the absolute value will always be positive.

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The simplified form of the expression is 2.4 x 10⁻⁶.

Expression:

An expression is the sentence with a minimum of two numbers/variables and at least one math operation in it.

Given,

Here we have the expression

[tex]\frac{7.2\times10^{-8}}{3\times 10^{-2}}[/tex]

Here we need to simplify this expression.

Here we have to divide this expression first,

Then we get,

[tex]= > \frac{7.2}{3}\times\frac{10^{-8}}{10^{-2}}[/tex]

First, we have to divide the numbers term then we get,

=> 7.2/3 = 2.4

Then we have to solve the exponential form,

For that we have to move the denominator value to upper term,

Then we get,

=> 10⁻⁸ x 10²

=> 10⁻⁸⁺²

=> 10⁻⁶

So, the simplified form is, 2.4 x 10⁻⁶.

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∠ AEC = ∠ DEB by using the property of the straight lines.

We are given the two lines AB and CD.

We are given that they intersect at point E and both are the straight lines.

Now, we know that, the sum of angles of a straight line will be equal to 180° (straight line property).

Now, For line AB, we get that:

∠ AED + ∠ DEB = 180°    …(1)

For line CD, we get that,

∠AED + ∠ AEC = 180°   … (2)

Now, we will subtract (1) from (2) and we get that:

∠ AED + ∠ DEB - ∠AED - ∠ AEC = 180° - 180°

∠ DEB - ∠ AEC = 0

∠ DEB = ∠ AEC

∠ AEC = ∠ DEB

Hence proved.

Therefore, we get that, ∠ AEC = ∠ DEB by using the property of the straight lines.

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Using divisibility rules, it is found that there are 165 members in the band.

The number of students in the last row gives the remainder of the division of the total number of members by the number of members in each row.

Hence:

It is also stated that the band has fewer than 200 members.

From the third bullet point, the possible values, that is, values that when divided by 8 have a remainder of 5, are given as follows:

{5, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 117, 125, 133, 141, 149, 157, 165, 173, 181, 189, 197}.

The number is 165, because:

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Answer:

the total sales are 361 sales a week i did this i got a 100

Answer:

2 feet

Step-by-step explanation:

Answer:

3.5

Step-by-step explanation:

6 plus 2 equals 8 and if you add 2 to 1.5 you get3.5

Given the information on the problem, we can use the law of cosines to find the length of p with the following equation:

substituting the values at hand, we get the following:

therefore, the length of p is 111 cm

B  = [tex]\left[\begin{array}{ccc}-1&3&2\\2&4&7\end{array}\right][/tex]  if A-B = C and values of A and C is given .

Calculation:

since A-B=C

   so, A-C=B

plugging in the values :-

 [tex]\left[\begin{array}{ccc}-2&2&0\\-5&7&9\end{array}\right] \left[\begin{array}{ccc}-1&-1&-2\\-7&3&2\end{array}\right][/tex]    = B

B  =  [tex]\left[\begin{array}{ccc}-1&3&2\\2&4&7\end{array}\right][/tex]

Hence the value of B is =  [tex]\left[\begin{array}{ccc}-1&3&2\\2&4&7\end{array}\right][/tex]

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The difference in the latitudes of Athens, Greece, Latitude 38° N, and Sydney, Australia, latitude 34° S is 72° .

We have two different coordinates, 38° N and  34° S

We can find the differnce in two different coordinates by following a few steps.

We have to consider South as negative North. So, we can write 34° S as -34° N.

Hence, we can determine the difference in between two coordinates.

Difference in coordinates ≡ 38° N - 34° S  = 38° N - ( - 34° N ) = 38° N + 34° N = 72°  N

So, we can conclude that, the difference is 72°.

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Answer:

60 minutes

Step-by-step explanation:

    Number of problems done, and the time taken to finish them are in proportion.

Let the time taken to finish 40 problems = 'x'

30 : 45 = 40 : x

Product of extremes = 30 *x = 30x

Product of means = 45 * 40

Product of extremes = Product of means

                30 *x    = 45 * 40

                          [tex]\sf x = \dfrac{45*40}{30}[/tex]

                         x = 15 * 4

                          x = 60 minutes

Given:-

To find the resultant value of the sum of the equation.

Answer:

3[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{3}[/tex] × [tex]\sqrt{6}[/tex]

= [tex]\sqrt{3(6)}[/tex]

= [tex]\sqrt{18}[/tex]

= [tex]\sqrt{9(2)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex]

= 3[tex]\sqrt{2}[/tex]