In your own words, explain the relationship between the graph of a function and the graph of function's derivative.

The total pounds of apples that Chris must pick before Pam’s orchard is cheaper that David's is 14.

The first step is to determine the total cost of picking apples from both orchards.

Cost of picking apples from David's Orchard : (10 x $2) + [(x - 10) x $1]

$20 + $x - $10

= $10 + $x

Cost of picking apples from Pam's Orchard : $10 + ($10 x $1.5) + [(x - 10) x 0.75]

$10 + $15 + 0.75x - 7.5

= $17.50 + 0.75x

When  Pam's Orchard is cheaper, the equation becomes :

$10 + $x  > $17.50 + 0.75x

$x - 0.75x > $17.50 - $10

0.25x > $7.50

x > $7.50 / 2.5

x > 3

Total pounds should be greater than 3, so it can be 4.

Total pounds = 10 + 3 = 14

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Answer:

solving the bracket

x×x = x²

x×-4= -4x

3×x= 3x

3×-4= -12

x²-x-12=0

Answer:

16

Step-by-step explanation:

4/5=0.8

20*0.8=16

Answer:

b -3

Step-by-step explanation:

t-3(4-t)=-24 multiply

t-12+3t=-24 simplify

4t-12=-24 plus 12 on both side

4t=-12 divide 4 on both side

t=-3

The division equation that represents number of 3/8 in 5/4 is 10/3 = x.

Given,

Fractions : 3/8 and 5/4

We have to find a division equation for number of 3/8 in 5/4

Number of 3/8 in 5/4 = x

Now,

Number of a in b = b/a

So here,

Number of 3/8 in 5/4, x = 5/4 / 3/8

Number of 3/8 in 5/4, x = 5/ 3/2

Number of 3/8 in 5/4, x = 5 × 2 / 3

Number of 3/8 in 5/4, x = 10/3

That is,

The division equation that represents number of 3/8 in 5/4 is 10/3 = x.

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The blue ribbon is 2.2 times longer than the orange ribbon

From the information given, we have that;

Now, lets convert the mixed fractions to improper fractions;

Length of orange ribbon = 95/12

Length of blue ribbon = 209/12

The ratio is expressed as;

Length of blue ribbon/length of orange ribbon

Substitute the values, we have;

= 209/12 ÷ 95/12

Take the inverse of the divisor and multiply

= 209/ 12 × 12/95

= 2. 2 times

Hence, it is 2.2 times longer.

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Using an arithmetic sequence, the number of design that the artist should use is:

b. Design 6.

In an arithmetic sequence, the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the rule presented as follows:

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

In which [tex]a_1[/tex] is the first term of the sequence.

The sequence for the number of circles is:

(4, 6, 8, ...)

Hence the common difference is given by:

d = 8 - 6 = 6 - 4 = 2.

Then the rule for the nth term is:

[tex]a_n = 4 + 2(n - 1)[/tex]

As the first term is of 4.

The maximum number is of 15 shaded circles, hence:

4 + 2(n - 1) ≤ 15

4 + 2n - 2 ≤ 15

2 + 2n ≤ 15

2n ≤ 13

x ≤ 6.5.

Hence the maximum number is of 6, meaning that Design 6 is chosen, given by option b.

The complete problem is given by the image at the end of the answer.

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We can represent the length in Zach's car model by x

Since we have been given that Ginny's car is 2 more than 3 times the length of Zach's car, then we can get the expression as follow

Therefore,

Ginny's model will be 2 + 3x

Next, we are told that the sum of the lengths of both cars is 30 inches

Then

Therefore,

The answer is

Thus, the answer is Option B

Step-by-step explanation:

[tex] \frac{5}{6} (a) - 3 = \frac{5}{8} \\ lcd = 48 \\ \\ \frac{5}{6} (a)(48) - 3(48) = \frac{5}{8} (48) \\ 40a - 144 = 30 \\ 40a = 30 + 144 \\ 40a = 174 \\ \frac{40a}{40} = \frac{174}{40} \\ a = 4\frac{14}{40} \\ a = 4 \frac{7}{20} [/tex]

I FIRST FOUND THE LCD AFTER THAT MULTIPLY EACH AND EVERY TERM IN THE EQUATION BY IT TO HET RID OF THE FRACTIONS AND SOLVE FOR a.

Answer: 89%

[tex]\frac{0.89}{1}*\frac{100}{100} = \frac{89}{100}[/tex]

Answer: The answer is the $42 T-Shirts

Step-by-step explanation: 42 divided by 4 is 10.5 dollars per t-shirt.

25 divided by 2 would mean 12.5 dollars per t shirt. There is only a 2 dollar difference, but it is clear that the 4 t-shirt deal is the best.

Answer:

x: (40,0)

y:(0,30)

Step-by-step explanation:

hope this helped

have a good day :)

The next correct step of the following elimination method is (C) subtract to eliminate 'x'

So, the next correct step of the elimination method:

Then, option (A) and option (D) is incorrect.

Thus, the correct option will be an option (C).

Therefore, the next correct step of the following elimination method is (C) subtract to eliminate 'x'

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From the given sequence, it is found that:

a) It is a geometric sequence, as the ratio between consecutive terms is the same.

b) Station 5 will be completed in 48 minutes.

c) Station 9 will be completed in 768 minutes.

In a geometric sequence, the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by the following rule:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In the context of this problem, the ratio between consecutive terms is given by:

r = 24/12 = 12/6 = 6/3 = 2.

Hence it is a geometric sequence.

Applying the recursive formula, the time for Station 5 is the time for Station 4 multiplied by the common ratio of 2, hence:

24 x 2 = 48 minutes.

The first term of the sequence is of 3, hence the explicit formula is given by:

[tex]a_n = 3(2)^{n-1}[/tex]

Hence the time for the 9th station, in minutes, is given as follows:

[tex]a_9 = 3(2)^{8} = 768[/tex]

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Our strategy to win $200 is to use $100 in just one chance. It is the best bet for winning $200.

Given that we start with $100 at a casino and can bet any amount of that particular money to play a game to any amount of times where we have a 40% chance of winning in each game. If we win, we will gain the amount we bet and return the amount that we bet. If we lose, we will lose our bet.

It has been asked that what should be our strategy to win get $200.

We can write from the given information that:

Probability of wining = 40 % = 0.4

Probability of losing = 1 - 0.4 = 0.6

The best bet to win $200 is to bet $100 in one go itself.

For the above bet chance of winning $100 is 0.4

But let us assume that we are betting $50 two times,

Then L-Lose and W-Win

There will be 4 rational possible cases (WW,WL,LW,LL)

Probability of all the 4 above given cases will be as follows:

Probability of (WW) = 0.4 X 0.4 = 0.16

Probaility of (WL) = 0.4 X 0.6 = 0.24

Probability of (LW) = 0.6 X 0.4 = 0.24

Probability of (LL) = 0.6 X 0.6 = 0.36

Now for winning $100 we need to win both the bets of $50.

But the probability of winning both the bets = 0.16 ( very less than 0.4)

Hence the best bet would be to use $100 in one chance itself.

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Our strategy to win $200 is to use $100 in just one chance. It is the best bet for winning $200.

It has been asked that what should be our strategy to win get $200.

We can write from the given information that:

Probability of wining = 40 % = 0.4

Probability of losing = 1 - 0.4 = 0.6

The best bet to win $200 is to bet $100 in one go itself.

For the above bet chance of winning $100 is 0.4

But let us assume that we are betting $50 two times,

Then L-Lose and W-Win

There will be 4 rational possible cases (WW,WL,LW,LL)

Probability of all the 4 above given cases will be as follows:

Probability of (WW) = 0.4 X 0.4 = 0.16

Probability of (WL) = 0.4 X 0.6 = 0.24

Probability of (LW) = 0.6 X 0.4 = 0.24

Probability of (LL) = 0.6 X 0.6 = 0.36

Now for winning $100 we need to win both the bets of $50.

But the probability of winning both the bets = 0.16 ( very less than 0.4)

Hence the best bet would be to use $100 in one chance itself.

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Answer:

13 cm

Step-by-step explanation:

You can use the pythagorean theorem to solve this problem. The pythagorean theorem states that [tex]a^2+b^2=c^2[/tex] where and b are the legs of a right triangle and c is the hypotenuse.

In the problem, we are given two legs, 12 and 5, so we can substitute them in for a and b and solve from there:

[tex]5^2+12^2=c^2[/tex]

[tex]25+144=c^2[/tex]

[tex]c^2=169[/tex]

[tex]c=13[/tex]

The missing side is 13 cm long

The distance between the two points is 10 units and the slope of the line is -78/25

To find the distance between two points, we can simply use the formula of distance between two which is given as

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

Let's substitute the values and solve for the distance.

[tex]d=\sqrt{(y_2-y_1)^2 + (x_2 - x_1)^2}\\d = \sqrt{(1-7)^2 + (-3 - 5)^2} \\d = 10[/tex]

2)

The slope of the line can be found using the two points given.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\[/tex]

let's substitute the values and solve.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\\\m = -\frac{78}{25}[/tex]

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Answer:d

Step-by-step explanation:

The answer after its estimation will be 3,00,00,000.

Here, the 53,320 will be estimated to 50,000 and 599 will be estimated to 600.

So, on multiplying, we get;

50,000×600 = 3,00,00,000

To offer an estimated, projected result rather than an exact result, we employ approximations in our calculations. Calculations are easier to handle when they are estimated using round numbers.

The result of rounding 109 to the closest ten is 110. and 100 is the nearest hundred. 2) Round the number downward if it is followed by the digits 0, 1, 2, 3, or 4. 102, for instance, is 100 when rounded to the closest ten.

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Answer:

y = -1/2x + 6.

Step-by-step explanation:

The line perpendicular to y = 2x + 3 has slope of - 1/2 so we can write it as

y = -1/2x + c

When x = -4, y = 8 so we substitute:

8 = -1/2 (-4) + c

8 = 2 + c

c = 8-2 = 6

So, the answer is

y = -1/2x + 6.

Answer:

y = -1/2x + 6.

Step-by-step explanation:

The club has to send 57 coupons to existing members.

Given,

The number of coupons sent out by a new club to boost sales for next year's membership = 152

They provide 3 times as many to potential members than to existing members

We have to find the number of coupons they send to existing members;

Here,

x be the number of coupons to existing members.

Then,

3x = 152

Now,

x = 152/3 = 50.66 ≈ 57

That is,

The club has to send 57 coupons to existing members.

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Answer: b=116, c=64

Step-by-step explanation:

The cost of each ticket is 8.9 dollars.

What is cost price?

In mathematics, the term cost price can be explained with the help of profit which states, as the amount which is on the commodity and in the form of standard price called cost price. For the profit, the amount of the commodity can be designed by the shopkeeper which is bigger amount as per the cost price.

According to the question, the Jason bought 4 tickets for basket ball game. He paid a total cost of $42.10 for the tickets and for parking as $6.50

The paid amount for the 4 tickets is: $42.10.

And the parking cost is: $6.50

Total cost price without parking is: $42.10 - $6.50 = $35.60

Therefore, to calculate the cost of each ticket is: 35.60/4 = 8.9 dollars

Hence, the cost of each ticket is 8.9 dollars.

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If the number were written in scientific notation, the exponent will be -2.

Scientific notation is a method of expressing numbers that are either too large or too little to be represented in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form.

The number of times a number is multiplied by itself is referred to as its exponent.

In this case, the mass of a textbook is approximately 0.0165 metric tons. It should be noted that this will be 1.65 × 10^-2. The exponent is -2.

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Answer: Multiply 102 by 8.82 = 899.64x

Answer: 3a

Step-by-step explanation: 4a - 1a = 3a

The measure of the acute angles in the triangle are 7.5 and 82.5

From the question, we have the following parameters:

One acute angle is 11 times the measure of the other acute angle.

Let the acute angles be x and y

Such that

y = 11x

The sum of the acute angles in a right triangle is 90

So, we have

x + y = 90

This gives

x + 11x = 90

So, we have

12x = 90

Divide by 12

x = 7.5

Recall that y = 11x

So, we have

y = 11 x 7.5

Evaluate

y = 82.5

Hence, the acute angles are 7.5 and 82.5

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Answer:

800000

Step-by-step explanation:

(1 x 10^1) = 10

(8 x 10^4) = 80000

10 x 80000 = 800000