Use left rectangles and Δ x = 0.5 to approximate the area under f ( x ) = 2 x 2 + 6 from x = 2 to x = 4 . Give one decimal place in your answer.

The total number of calories burned can be represented by the inequality 10x + 15y ≥ 600

Using the following parameters:

The inequality is

10x + 15y ≥ 600

In this case, x = 30 and y = 0.

Plugging in these values into the inequality:

10(30) + 15(0) = 300

Since 300 is less than 600, Timmykat will not burn enough calories if he only bikes for 30 minutes and doesn't run at all.

In this case, x = 0 and y = 30.

Plugging in these values into the inequality:

10(0) + 15(30) = 450

Since 450 is less than 600, Timmykat will not burn enough calories if he only runs for 30 minutes and doesn't bike at all.

See attachment

Three different scenarios where Timmykat will burn at least 600 calories a day are:

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Answer:

42 divided by 6=7 so in each vase there are 7 flowers

Step-by-step explanation:

it depends on what x is but simplified that equation is 9x+9+x

Hello:

 --> this problem wants us to calculate the slope between (5, -6) and (2, 3)

So we are given two points:

  --> (x1, y1): (5, -6)

  --> (x2,y2): (2, 3)

Let's consider our formula needed:

 [tex]\text{Slope} = \dfrac{y2-y1}{x2-x1}=\dfrac{3--6}{2-5} =\dfrac{9}{-3} =-3[/tex]

Thus our slope is -3

Answer: -3

I am pretty sure the answer is 14.5

Answer:

14.5

Step-by-step explanation:

Arrange the numbers from small to big

11, 11, 12, 13, 14, 15, 16, 16, 18, 20

If the set of data is an even number, like in this case,

Take 2 of the middle numbers:

14 and 15

Add them and divide by 2:

14+15= 29

29 ÷ 2= 14.5

We have compared the given standard distributions based on their means and standard deviations.

What is the standard deviation?

Standard deviation is a statistical measure of the spread of a dataset, defined as the square root of its variance. It is a way to quantify the amount of variation or dispersion of a set of data values.

(a) The means and the standard deviations of both distributions (1) and (2) are the same. The only difference is that there is an outlier in (2) with the value of 20 that doesn't exist in (1)

(b) The means of both distributions (1) and (2) are the same. However, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)

(c) The means of both distributions (1) and (2) are different, Distribution (2) has larger mean than Distribution (1). Also, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)

(d) The means of both distributions (1) and (2) are different, Distribution (2) has smaller mean than Distribution (1). Also, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)

Hence, we have compared the given standard distributions based on their means and standard deviations.

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Answer:

Width = 3.773 inches

Length = 79.227 inches-

Step-by-step explanation:

g = 7(3w)             Eq. 1

166 = 2(g+w)       Eq. 2

g = length

w = width

From Eq, 1:

g = 21w              Eq. 3

Replacing Eq. 3 in Eq. 2

166 = 2(21w + w)

166 = 2(22w)

166 = 44w

166/44 = w

w = 3.773

From Eq. 3

g = 21(3.773)

g = 79.227

Check:

From Eq. 2:

166 = 2(79.227 + 3.773) = 2 * 83

The inverse function of f (x) = 1/3x - 2 is f⁻¹(x) = 3(x + 2), the value of a is 3, and the value of x-intercept is x = -2.

To find the inverse of the given function as it is not a one to one function (has the same value f(x) for more that one value of x) you restrict the domain to get a function one to one.

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

f (x) = 1/3x - 2

Find its inverse as shown below,

Add 2 to x and then divide by 1/3 as shown below,

f⁻¹(x) = (x + 2) / 1/3

f⁻¹(x) = 3(x + 2)

compare with f⁻¹(x) = a (x + 2)

a = 3

Calculate the x-intercept by putting f(x) = 0

0 = x + 2

x = -2

In a quadratic function as given use the vertex to restrict the domain; restrict the domain using coordinate x of the vertex.

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Step-by-step explanation:

after mixing 1 can of concentrate and 3 cans of water, we will have 4 cans of juice.

the volume of 1 can is (as for any cylinder or regular 3D object)

base area × height

for a cylinder the bar area is the area of a circle

pi×r²

r is the radius, which is half of the diameter.

in the picture it is not fully clear what is 2.25 in long : the diameter of the radius ?

I suspect it is the diameter.

so, the radius of our cans is 2.25/2 = 1.125 in

the volume of 1 can is

pi×1.125²×4.25

and the volume of all 4 cans of juice is then

4×pi×1.125²×4.25 = 17×3.14×1.265625 = 67.5590625 in³

≈ 68 in³

so, your answer is 68.

The functions are 0, -2 and 1 for the mentioned function is 4, - 16 and 2.

Firstly we will represent the function in equation form. Then we will calculate the result by keeping each value of function.

f(x) = x³ - 3x² + 4

Calculating result when function is 0

f(x) = 0³ - 3×0² + 4

f(x) = 0 - 0 + 4

f(x) = 4

Calculating result when function is -2

f(x) = (-2)³ - 3×(-2)² + 4

Finding square and cube

f(x) = -8 - 3×4 + 4

Performing multiplication

f(x) = - 8 - 12 + 4

Performing addition

f(x) = - 20 + 4

Performing subtraction

f(x) = - 16

Calculating result when function is 1

f(x) = 1³ - 3×1² + 4

f(x) = 1 - 3 + 4

Performing addition

f(x) = 5 - 3

Performing subtraction

f(x) = 2

Thus, functions are 4, -16 and 2.

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To make a 1-ounce tube of the ointment that is 4% hydrocortisone, the pharmacist needs to use 0.04 ounces of the active ingredient (hydrocortisone).

The pharmacist has 1% and 5% concentrations in stock, therefore he needs to use 0.96 ounce of the 1% concentration and 0.04 ounces of the 5% concentration.

The pharmacist should use 0.96 ounces of the 1% concentration and 0.04 ounces of the 5% concentration to make a 1-ounce tube of the ointment with the correct percentage of hydrocortisone.

It's important to note that it's important that the pharmacist needs to mix the correct amount of hydrocortisone to get the desired percentage, and also that the pharmacist needs to check the final percentage of the ointment before dispensing to ensure the safety and efficacy of the medication.

The inequality that represents Kenny's situation is 25x ≤ 500 − 200

In mathematics, inequality is describe about the relative size or order of two values.

It states that one value is either greater than, less than, or not equal to the other value.

It is usually represented by symbols such as > (greater than), < (less than), ≥ (greater than or equal to), ≤ (less than or equal to), and ≠ (not equal to).

In this question ,

Let x be the number of basketballs Kenny needs to buy.

The inequality that represents Kenny's situation is:

25x ≤ 500 − 200

This inequality states that the total cost of purchasing the basketballs (25x) must be less than or equal to the available balance minus the desired amount after purchase (500 − 200 = 300).

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Answer:

Step-by-step explanation:

2. 63

3. 0

4. 6

5. 9

6. 10

7. 4

8. 8

9. 0

10. 5

11. 10

12. 7

13. 9

14. 5

15. 5

16. 3

17. 8

18. 0

Answer: 20 different total voting combination

Step-by-step explanation: So we have 5 bands. Lets called them A, B, C, D, and E.

If John has to vote on his favorite and second favorite that means we will be selecting 2 bands out of the 5 possible to choose from.

To find the TOTAL amount of different combinations we need to pair up bands and find all the combo's.

Here are the results/totals:

AB

AC

AD

AE

BA

BC

BD

BE

CA

CB

CD

CE

DA

DB

DC

DE

EA

EB

EC

ED

So this is 20 different total voting combinations.

If you want to do it simpler without listing you can take the the 5 bands and multiple by 4 since you know each initial band (A, B, C, D, and E) will be paired with another band other than itself.

If a submarine is 575 feet below sea level and is ascending at a rate of 325 feet per minute, we can use that information to determine how long it will take for the submarine to reach the surface.

The distance the submarine needs to travel to reach the surface is:

Distance = Sea level - Current depth

Distance = 0 feet - (-575 feet) = 575 feet

We can use the rate of ascent and distance to find the time it will take for the submarine to reach the surface.

Time = Distance / Rate

Time = 575 feet / 325 feet per minute

Time = 1.77 minutes

So it will take the submarine 1.77 minutes to reach the surface, assuming it continues to ascend at a rate of 325 feet per minute.

Answer: No, it is not a right triangle

Step-by-step explanation:

a=17

b=16

c=26

a^2 + b^2 = c^2 (C will always be the longest side)

17^2 + 16^2 = 26^2

49 + 256 = 676

305 is not equal to 676

Answer:

to test if this is a right triangle, test the side lengths with the Pythagorean theorem

a^2 + b^2 = c^2

Step-by-step explanation:

c is the hypothenuse, the longest side of a right triangle

a and b are the legs of the right triangle.

a = 16

b = 17

c = 26

16^2 + 17^2 = 26^2 ?

256 + 289 = 676?

545 ≠ 676

NO, this triangle is NOT a right triangle

Alex's set of ordered pairs would no longer define a function if any of the following actions were taken:

A set of ordered pairs defines a function if, for every element in the domain (the set of first coordinates), there is exactly one element in the range (the set of second coordinates).

For example, if Alex's set of ordered pairs is {(1,2), (2,3), (3,4)}, it would no longer define a function if a new ordered pair of (2,5) is added to it, as it would mean that there are now two different second coordinates (3,5) for the first coordinate 2. This would violate the rule that every element in the domain must have exactly one corresponding element in the range. Similarly, removing one of the ordered pairs, changing the order of the ordered pair, or changing the domain or range would cause the set to no longer to define a function.

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The concession stand charges $2.25 for each nacho.

What is the percentage?

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" is also used. A percentage is a dimensionless number; it has no unit of measurement.

To find out how much the concession stands charge for each nacho, we need to calculate the markup percentage.

The markup percentage is calculated by:

(Markup Amount / Cost) * 100 = Markup Percentage

In this case, the markup amount is 80% of the cost of each nacho, which is:

(80/100) * $1.25 = $1

So, the markup amount is $1.

To calculate the final price of each nacho, we need to add the markup amount to the cost:

$1.25 (cost of nacho) + $1 (markup amount) = $2.25

Therefore, the concession stand charges $2.25 for each nacho.

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Answer:

a. -0.004
b. -sqrt(20)/70

Step-by-step explanation:

a.

We are given that y = a(x - 70)^2 + 20

And we know that x=0 and y=0

We can substitute these values into the equation:

0 = a(-70)^2 + 20

Simplifying we get:

0 = a(4900) + 20

Subtracting 20 from both sides we get:

-20 = a(4900)

Dividing both sides by 4900 we get:

a = -20/4900

a = -20/4900 = -0.004

So the value of a is -0.004

b.
We are given that y = a(x - 70)^2 + 20

And we know that x=140 and y=0

We can substitute these values into the equation:

0 = a(140-70)^2 + 20

Simplifying we get:

0 = a(70)^2 + 20

Subtracting 20 from both sides we get:

-20 = a(70)^2

Taking the square root of both sides:

sqrt(-20) = a(70)

Dividing both sides by 70:

-sqrt(20)/70 = a

a = -sqrt(20)/70

So the value of a is -sqrt(20)/70

Answer: 69

Step-by-step explanation:

The data set's environment variable(s) are quantified on a nominal scale.

Describe data sets?

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Answer:

We can solve this problem using the principle of counting, specifically the handshaking lemma.

The handshaking lemma states that in a group of 2n people, where each person shakes hands with exactly one other person, the number of handshaking arrangements is equal to n!.

In this case, we have 9 people, so n = 4.5. Each person shakes hands with exactly two other people, so the number of handshaking arrangements is (4.5!) / (2!)^4 = 945.

Finally, the remainder when N is divided by 1000 is 945 % 1000 = 945.

Step-by-step explanation:

The standard deviation of random variable K is 15.49  (option D ) and this can be determined by using the formula of mean and standard deviation.

Given,

The mean of geometric distribution of random variable K = 16

Formulae for finding mean,

                                      mean = 1/p

Substitute the value of the mean in the above formula in order to determine the value of 'p'.

[tex]16 =\frac{1}{p}[/tex]

[tex]p = 0.0625[/tex]

The formulae for standard deviation :

   S.D.=[tex]\frac{\sqrt{1-p} }{p}[/tex]

Now substitute the value of p in the above equation,

S.D. [tex]= \frac{\sqrt{1-0.0625} }{0.0625}[/tex]

       [tex]= 15.49[/tex]

Hence, the answer is option D.

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Let H be a nontrivial subgroup of G.

Since p and q are coprime, the only possible divisors of pq are p and q. Thus we must have either |H|=p or |H|=q. Now, by Cauchy's theorem, H must contain an element of order p or q respectively. Then, by Lagrange's theorem, the order of any element in H must divide p or q, i.e. H must be cyclicThen, H has an order of m, where m is a divisor of pq. By Lagrange's Theorem, m divides both p and q. Since p and q are prime, m must be equal to either p or q. This implies that the order of H is either p or q.

Therefore, H must be cyclic, because the order of a cyclic group is always equal to its number of elements. Thus, any nontrivial subgroup of G must be cyclic.

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Complete question:If G is a group of order pq, where p and q are primes, how could I prove that any nontrivial subgroup of G must be cyclic?

The greatest prime factor of 2516 is 11, so the answer is A. 11

What is the prime factor?

A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11,

We can use the process of counting to find the sum of all the numbers in S.

For one-digit numbers, there are 2 possibilities (0 or 1).

For two-digit numbers, there are 2 x 2 = 4 possibilities (00, 01, 10, 11).

For three-digit numbers, there are 2 x 2 x 2 = 8 possibilities (000, 001, 010, 011, 100, 101, 110, 111).

For four-digit numbers, there are 2 x 2 x 2 x 2 = 16 possibilities (0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111).

So, the sum of all the numbers in S is

2 + 4(1+2+3+4) + 8(1+2+3+4+5+6+7+8) + 16(1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16)

We can simplify this expression as

2 + 4(10) + 8(36) + 16(136)

The sum of all the numbers in S is equal to 2 + 40 + 288 + 2176 = 2516.

Hence, The greatest prime factor of 2516 is 11, so the answer is A. 11

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Answer: x= 0.146  or  x= -5.15

(refer to the steps I wrote down, check the image)

Answer:

Option A: (5,-2)

Step-by-step explanation:

4x - 3y = 26

3x + 2y = 11

from equ 1 make x the subject formular | equ means equation

4x - 3y = 26

4x = 26 + 3y

x = (26 + 3y)/4

Substitute x = (26 + 3y)/4 into equ 2

3((13+3y)/4) + y = 11

(39+17y)/4 + y = 11

39/4 + 17y/4 + y = 11

39/4 + 17y/4 = 11

17y/4 = 11 - 39/4

17y/4 = -17/2

17/4y/17/4 = -17/2/17/4

y = -2

Substitute y = -2 into equ 2

3x + 2y = 11

3x + 2(-2) = 11

3x - 4 = 11

3x = 11 + 4

3x = 15

3x/3 = 15/3

x = 5

(x,y) = (5,-2)

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Answer:

30

Step-by-step explanation:

Answer: 30

Step-by-step explanation:

Use  Pythagorean theorem a^2 + b^2 = c^2:

18^2 + 24^2 = c^2

324 + 576 = c^2

900 = c^2

c = 30

Answer: The answer is: 525 millimeters of compound A are needed.

Step-by-step explanation:
You have to put it in equation form to solve for compound A. To do this use variables.

7(x) + 5(x) = 900
12(x) = 900
x = 900/12
x = 75
When we get 75 you have to plug it into compound A to get this:
7(75) = 525

To confirm our answer we plug in 75 to both variables.
7(75) + 5(75) = 900

I hope this was able to help you :D

If the consumer buys both product X and product Y,  the consumer buy of each to maximize utility  will be 3X and 4Y.

Product X                         Product Y

Quantity   MUx  Quantity   MUy  

1                  32              1                    24

2                  28            2                    20

3                  24              3                     16

4                  20            4                       12

5                   16            5                      8

If the consumer can only buy product X, consumer buy and the total utility will be 5X and 120.

If the consumer buys both product X and product Y,  the consumer buy of each to maximize utility  will be 3X and 4Y.

When the consumer purchases the utility-maximizing

combination of product X and product Y, total utility will be 156.

A consumer is in equilibrium and is spending income in such a way that the marginal utility of product X is 40 units and Y is 16 units. The unit price of X is $5. The price of Y is: $2 per unit.

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The complete question is :

Based on the table below showing the marginal utility schedules for product X and product Y for a hypothetical consumer. The price of product X is $4 and the price of product Y is $2. The income of the consumer is $20. how much will the consumer buy of each in order to maximize utility?