If George’s mom needs 3 kilograms of sliced cheese for a family party, how many
packages will she need to buy?

In scenario a, the function c(x) represents the density of traffic on a straight road, measured in cars per mile, where x is the number of miles east of a major interchange. The product c(x) · Ax has units of cars, as it represents the number of cars in a certain segment of the road. The definite integral ∫ c(x) dx and its Riemann sum approximation given by 1/n ∑ c(xi) · Δx have units of cars per mile, as they represent the average density of traffic over a certain distance. When evaluating the definite integral ∫ c(x) dx, we get a value that represents the total number of cars on the road between two given points.

In scenario b, the function B(x) represents the distribution of the weight of books on a shelf, in pounds per inch, where x is the number of inches from the left end of the shelf. The product B(x) · Ax has units of pounds, as it represents the weight of books in a certain segment of the shelf. The definite integral ∫ B(x) dx and its Riemann sum approximation given by 1/n ∑ B(xi) · Δx have units of pounds, as they represent the total weight of books on the shelf. When evaluating the definite integral ∫ B(x) dx, we get a value that represents the total weight of books on the shelf.
a. i. The units on the product c(x) · Δx are cars per mile (from c(x)) multiplied by miles (from Δx), resulting in cars.

a. ii. The units on the definite integral and its Riemann sum approximation are the same as the units on the product c(x) · Δx, which are cars.

a. iii. To evaluate the definite integral, we have:

∫(200 + 100e^(-0.12x)) dx

Using the integral rules, we get:

[200x - (100/0.12)e^(-0.12x)] (evaluate this from 0 to a specific value to find the total cars between 0 and that value)

The meaning of the value is the total number of cars on the road between 0 miles and the specified value of x miles east of the major interchange.

b. i. The units on the product B(x) · Δx are pounds per inch (from B(x)) multiplied by inches (from Δx), resulting in pounds.

b. ii. The units on the definite integral and its Riemann sum approximation are the same as the units on the product B(x) · Δx, which are pounds.

b. iii. To evaluate the definite integral, we have:

∫(0.5 + (x+1)^2) dx

Using the integral rules, we get:

[0.5x + (1/3)(x+1)^3] (evaluate this from 0 to 72 to find the total weight of books on the shelf)

The meaning of the value is the total weight of the books on the 6-foot-long shelf.

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The area of the parallelogram is 1710 square inches

From the question, we have the following parameters that can be used in our computation:

Base = 38 inches

Side = 44 inches

Height = 35 inches

We can find the area of the parallelogram by multiplying the base (width) by the height

Using the above as a guide, we have the following:

Area = 38 * 45

Evaluate

Area = 1710

Hence, the area is 1710 square inches

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Answer:

Area of a parallelogram (base x height)

Area of the parallelogram = 38 x 35

Area of the parallelogram = 1,330 in.²

For all n ≥1, 10^n −1 is divisible by 9: the induction hypothesis, 10^k − 1 is divisible by 9. Therefore, 9 divides the second term. Also, 9 divides 9*10^k, since 9 is a factor of 9 and 10^k is a power of 10. Hence, 9 divides the entire expression 10^(k+1) − 1.

We will use mathematical induction to prove the statement. Base Case: For n = 1, we have 10^1 − 1 = 9, which is divisible by 9. Induction Hypothesis: Assume that for some positive integer k, 10^k − 1 is divisible by 9.

Induction Step: We need to show that if the statement is true for k, then it is also true for k+1. We have: 10^(k+1) − 1 = 10^k − 1 = 9^k + (10^k − 1)

By the induction hypothesis, 10^k − 1 is divisible by 9. Therefore, 9 divides the second term. Also, 9 divides 9*10^k, since 9 is a factor of 9 and 10^k is a power of 10. Hence, 9 divides the entire expression 10^(k+1) − 1.

As a result, we have demonstrated through mathematical induction that 10n-1 is divisible by 9 for all n.

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x = 2y+8

Step-by-step explanation:

3x-y = 14

3(2y+8)-y = 14

6y+24-y = 14

5y = 14-24

y = -10/5

y = -2

now,

x = 2y +8

x = 2(-2)+8

x = 4

Therefore, the value of x is 4 and y is -2.

Answer:

Approximately 1.6

Step-by-step explanation:

To graph. a function, let use desmos or graphing calculator.

Here the function.

The length of the pendulum as shown here when x=2, is 1.6

It is fine to use these data because the price sample is random so bias will not interfere with the results.

Based on the information, we can infer that it is correct to use the data from this sample because it is random, that is, it does not have a defined order. Therefore, it is not necessary to take bias into account because it will not have any influence on the results.

In accordance with the above, it would be incorrect to take the data from a non-random sample because information would be prioritizing and this would cause the results to be blinded.

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a) By looking at the picture, we can tell that the orange weighs 135 grams.

b) Now when we look at the picture, we see they have added an apple. The total weight is 250 grams. 250 grams - 115 grams, so the apple weighs 115 grams.

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

18

Step-by-step explanation:

You take 30% of 60 to find the number of brown beads.

The two inequalities that define the shaded region in the diagram are:

y ≥ 4 and y < x

For the solid vertical line, the slope (m) is 0. The inequality sign we would use would be "≥"  because the shaded region is to the left and the boundary line is solid.

The y-intercept is at 4, therefore, substitute m = 0 and b = 4 into y ≥ mx + b:

y ≥ 0(x) + 4

y ≥ 4

For the dashed line:

m = change in y / change in x = 1/1 = 1

b = 0

the inequality sign to use is: "<"

Substitute m = 1 and b = 0 into y < mx + b:

y < 1(x) + 0

y < x

Thus, the two inequalities are:

y ≥ 4 and y < x

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Only the trapezoid has one pair of parallel side while all the other quadrilateral( in this question) square, rhombus and rectangle has two pair of parallel sides.

Answer:

b

Step-by-step explanation:

The perimeter of the polygon is 4√(a² + b²).

Option D is the correct answer.

The distance between two points of a line is given as:

Distance = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

We have,

The polygon is formed by joining the four-point:

(0, b), (-a, 0), (a, 0), and (0, -b)

The distance between two points (x1, y1) and (x2, y2) is given by the formula:

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

Now,

Using this formula, we can find the lengths of the sides of the polygon:

The distance between (0, b) and (-a, 0) is d1.

= √[(0 - (-a))² + (b - 0)²]

= √(a² + b²)

The distance between (-a, 0) and (0, -b) is d2.

= √[(0 - (-a))² + (-b - 0)²]

= √(a² + b²)

The distance between (0, -b) and (a, 0) is d3.

= √[(0 - a)^2 + (0 + b)^2]

= √(a² + b²)

The distance between (a, 0) and (0, b) is d4.

= √[(0 - a)²+ (b - 0)^2]

= √(a² + b²)

The perimeter of the polygon is:

P = d1 + d2 + d3 + d4

= 4√(a² + b²)

Thus,

The perimeter of the polygon is 4√(a² + b²).

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Answer:

5

Step-by-step explanation:

\(Steps\\\\6+\left(-1\right)\\\\\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a\\=6-1\\\\\mathrm{Subtract\:the\:numbers:}\:6-1=5\\=5\)

Answer:

Formula for volume of cone;

V = π\(r^{2}\) * h/3

Now, to find the radius of the diameter you find 1/2 of the diameter.

(diameter/2 = radius).

2.

Height = 28

Diameter = 24

To find radius;

24/2 = 12, is the radius.

Now plug this into our formula:-

V = π\(r^{2}\) * h/3

V = 3.14(12^2) * 28/3

V = 3.14(144) * 9.333..

V = 452.16 * 9.333..

V = 4220.00928, which rounds to,

V = 4220

3.

Height = 12

Diameter = 11

To find the radius of the diameter you find 1/2 of the diameter.

(diameter/2 = radius).

11/2 = 5.5 is your radius.

Apply the same formula as mentioned earlier;

V = π\(r^{2}\) * h/3

V = 3.14(5.5^2) * 12/3

V = 3.14(30.25) * 4

V = 94.985 * 4

V = 379.94

(a) The total number of outcomes is 122

(b) The relative frequencies are Red = 26/122, Yellow = 15/122, Green = 44/122 and Blue = 37/144

(c) The expected number of green sour patch is 180

From the question, we have the following parameters that can be used in our computation:

The table of values

So, we have

Total = 26 + 15 + 44 + 37

Total = 122

This is calculated as

Relative frequency = frequency/total

So, we have

Red = 26/122

Yellow = 15/122

Green = 44/122

Blue = 37/144

Here, we have

Pieces = 500

So, we have

Green = 44/122 * 500

Evaluate

Green = 180

Hence, the expected number of green sour patch is 180

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Answer:

  (y -12)(y -4)

Step-by-step explanation:

This can be factored as the difference of squares:

  (y -8)² -16 = (y -8)² -4² = (y -8 -4)(y -8 +4) = (y -12)(y -4)

Answer:

Train A= 249 tons

Train B= 87 tons

Step-by-step explanation:

Total weight of Train A and Train B= 336 tons

Weight of Train A > Weight of Train B

Difference of their weights= 162 tons

Let the weight of Train A be t.

Then weight of Train B= t-162

Total weight= 336 tons

         t+t-162= 336

                 2t= 336+162

                 2t= 498

                   t= \(\frac{498}{2}\)

                   t= 249

t-162= 249-162

       = 87

∴ the weights of Train A and Train B are 249 tons and 87 tons respectively.

2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

To prove that the expression 2n^3 + 3n + 10 is in the set Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3), we need to show that the expression can be written in the form a(n^3) for some constant "a".

Let's start by factoring out the common factor of n^3 from each term:

2n^3 + 3n + 10 = n^3(2 + 3/n^2 + 10/n^3)

Now, let's rewrite the expression as a single term multiplied by n^3:

2n^3 + 3n + 10 = (2 + 3/n^2 + 10/n^3)n^3

Simplifying the expression inside the parentheses:

= (2n^3 + 3n^2 + 10n^3)/n^3

= (12n^3 + 3n^2)/n^3

= 12 + 3/n

ow, we can see that the expression can be written in the form a(n^3), where a = 12 and n^3 = 3/n.

Therefore, we have shown that 2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

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Answer: 150$

Step-by-step explanation:

60 minutes in an hour means you make 5$ * 6 = 30$ per hour.

For 5 hours would be 150$

Answer: 770

Step-by-step explanation:

It would= 10 x 77 and 77 x 10 it=770 because you always add a zero like this.

7 x 10=70

70 x 10=700

700 x 10=7,000

7,000 x 10=70,000

Or another example take 8

8 x 10=80

8 x 100=800

8 x 1,000=8,000

8 x 10,000=80,000

Hope it helps have a great day:)

Answer:

3

Step-by-step explanation:

The slope of the given line is \(\frac{2}{3}\).

If a line passes through two points (x₁, y₁) and (x₂, y₂) respectively, then slope of the line is \(m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

Here, the given line passes through points (0, 6) and (-9, 0).

Therefore, the slope of this line is (m)

\(= \frac{0 - 6}{-9 - 0}\\= \frac{6}{9} \\= \frac{2}{3}\)

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Q1 If you averaged every person in the population, the result would be Mu, but the mean of a sample, or xbar, would be the average value discovered in the sample.

Q2 For the group being tested, each point in a sample distribution represents a potential outcome variable.

Q3 The random condition is very important because it simplifies the sample and prevent possible bias in the sampling.

Q4 To make sure that the observations in the sample are nearly independent, it is crucial to evaluate the 10% condition before calculating probability involving x.

Q5 The big counts criterion ensures that there are more successes than failures for a normally distributed set of results. The need for big numbers is np ≥10 and n(1-p) ≥10.

Q6 For a variety of reasons, finding unbiased estimates for those seeking asylum may be challenging. First, because of persecution, these people are escaping their country.

Q7 there is less spread for larger sample than that of lower sample.

The probability distribution of a statistic acquired from a bigger sample size taken from a certain population is known as the sampling distribution.

Based on the data they have available, sampling distributions are useful tools used by researchers to estimate and draw conclusions about a wider population of interest.

Q1 If you averaged every person in the population, the result would be Mu, but the mean of a sample, or xbar, would be the average value discovered in the sample.

Q2 For the group being tested, each point in a sample distribution represents a potential outcome variable.

Q3 The random condition is very important because it simplifies the sample and prevent possible bias in the sampling.

Q4 To make sure that the observations in the sample are nearly independent, it is crucial to evaluate the 10% condition before calculating probability involving x.

Q5 The big counts criterion ensures that there are more successes than failures for a normally distributed set of results. The need for big numbers is np ≥10 and n(1-p) ≥10.

Q6 For a variety of reasons, finding unbiased estimates for those seeking asylum may be challenging. First, because of persecution, these people are escaping their country.

Q7 there is less spread for larger sample than that of lower sample.

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\(\dfrac{3^{15}}{3^3} = 3^{15 -3} = 3^{12}\)

The value of a and b given that the opposite side are equal are 17 and 6 respectively

The kite is a quadrilateral with 4 sides and the opposite side of the side are equal. If they are, then;

2a - 4 = 30
2a = 34

a = 17

Similarly

3b+6 = 24

3b = 18
b = 6

Hence the value of a and b given that the opposite side are equal are 17 and 6 respectively

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Answer:

y = -2

Step-by-step explanation:

using slope formula, you can create the following proportion:

y-(-1) = 1

-5-(-1)    4

cross-multiply:

4(y+1) = -4

4y + 4 = -4

4y = -8

y = -2

Equation/Question:

Solve for b. 3(b + -2)-8=-5 what is the answer?​

Answer/Steps to answer:

1.Simplify  b+-2 to b−2.

3(b−2)−8=−5

2. Add 8 to both sides.

3(b-2)=-5+8

3. Simplify  -5+8  to  3.

3(b-2)=3

4. Divide both sides by 3.

b-2=1

5. Add 2 to both sides.

b=1+2

6. Simplify  1+2 to 3.

b=3

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There are 70 different types of pizzas could be ordered

A permutation is an act of arranging the objects or numbers in order.

Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter

Given,

Number of options on crust=2

Number of options on topping= 7

Number of options on size= 5

Therefore for each type of crust there are 7 different topping, for each toppings there are 5 different sizes

The total number ways of ordering pizza=2×7×5=70

Hence, there are 70 different types of pizzas could be ordered

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