Mike bought 20 packets of chips for his birthday party.he kept 4 packets with him and distributed the remaining to his friends attending his party. After the party he discovered 3 unopened packets of chips. How many packets of chips has he got?

Answer:

4

Step-by-step explanation:

6 - 2 = 4

Answer: 4

The average of the given 5 equations is; x' = 2x - 1.6

In mathematics, average is also called the mean and it has the formula as;

x' = ∑fx/∑f

Now, we are given the equations as;

x + 3, 2x - 4, 3x - 6, 2x - 5, and 2x.

Thus;

∑fx = x + 3 + 2x - 4 + 3x - 6 + 2x - 5 + 2x

∑fx = 10x - 8

The number of expressions given is 5 and so ∑f = 5

Thus;

x' = (10x - 8)/5

x' = 2x - 1.6

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Answer:

96

Step-by-step explanation:

20 percent of 80 is 16, and added to 80 would equal 96

Answer:

-96

192

-384

Step-by-step explanation:

Multiply by negative 2

Answer:

12

Step-by-step explanation:

According to the question the fraction of the bigger square that is shaded is 50%.

Fraction is a numerical representation of a part of a whole or a ratio between two numbers. It is written in the form of a/b where a is the numerator and b is the denominator. A fraction can refer to a part of a whole number, a part of a set, or a part of a unit. Fractions are commonly used in mathematics, cooking, science, and many other areas.

This is because the ratio of the area of the smaller square to the area of the bigger square to the area of the triangle is 1:3:2. Therefore, the ratio of the area of the shaded parts of the squares to the area of the shaded triangle is 25%: 25%:50%. Since the area of the bigger square is three times that of the smaller square, then 50% of the bigger square must be shaded to maintain the given ratio.

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Answer:

2(x - 2) = 8

x = 6

Step-by-step explanation:

2(x - 2) = 8

2(x - 2) = 8

2x - 4 = 8

     +4   +4

-----------------

2x = 12

÷2   ÷2

----------

x = 6

I hope this helps!

Hello!

50 sheets => 50mm

1 sheet => 50mm/50 = 1mm

1mm = 0.1cm

the answer is 0.1cm

Answer: 0.1

Step-by-step explanation:

1mm=0.1cm

So each sheet is 0.1cm

Use the formula,

I = Prt

P = Principal amount = 400

I  = interest = 18

r = annual rate

t = time in years = 9/12 = 3/4

so,

18 = 400*r*3/4

r =  0.06

so the annual interest rate is 0.06 or 6%.

Answer:

x2 - 2x - 15 = 0

(x - 5)(x + 3) = 0

x = 5 or x = -3

Since x is a positive integer, x = 5

Therefore, the sides of the triangle are 5 cm, 12 cm and 13 cm.

Answer:

the slope is the factor of x = (_5)

1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces

Answer:

Step-by-step explanation:

Expression given:

Find its value when g = 10:

\(Answer:\)

The median is $\(40,000\)

To find a median, find the averaging number, rather the middle number.

The middle number will always be your answer.

Answer:

Step-by-step explanation:

-3g - 2 + 4g - 10

g - 2 - 10

g -12

Bearing is measured from reference line clockwise or counter-clockwise - FALSE.

A bearing is an angle that is calculated clockwise from the north.

The vertical angle between an object's direction and either north or another object is known as a bearing or azimuth in navigation. You can specify the angle value in a number of different angular units, including degrees, mils, and grad.

Angles are measured in comportments clockwise from north.

The direction of north must be identified before taking a bearing measurement.

The math exam question will typically include this north direction. The required angle is then measured in a clockwise fashion. Since all bearings must be reported in three figures, we must begin the three-figure bearing with zero if the angle measured is less than 100 degrees.

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1) The demand for good 1 is 10/(5√2) and the demand for good 2 is 50√2/2.

2) The demand for good 1 is e5 and the demand for good 2 is e2.

3) The tax revenue the government collects from the consumer is 0.16e5.

4) The demand for good 1 is m/p₁ and the demand for good 2 is m/p₂.

Question 1: If the consumer has the utility function u(x₁, x₂) = √(x₁x₂) and has an income of m = 10, the demand for the two goods can be found using the following equation:

MRSxy = Px/Py

Where MRSxy is the Marginal Rate of Substitution between goods x and y, Px and Py are the prices of goods x and y respectively.

Therefore, for this problem we have MRST1,2 = 1/5 and P₁ = 1, P₂ = 5. Solving for the demands x₁ and x₂, we get:

x₁ = 10/(5√2), x₂ = 50√2/2

Therefore, the demand for good 1 is 10/(5√2) and the demand for good 2 is 50√2/2.

Question 2: If the consumer has the utility function u(x₁, x₂) = 1/2 ln x₁ + 1/2 ln x₂ and has an income of m = 10, the demand for the two goods can be found using the same equation as in Question 1. In this case the MRST1,2, P₁, and P₂ are the same as in Question 1. Thus, solving for the demands x₁ and x₂, we get:

x₁ = e5, x₂ = e2

Therefore, the demand for good 1 is e5 and the demand for good 2 is e2. This is different than the demands found in Question 1, because the utility functions are different. The Square Root utility function in Question 1 implies that the consumer has diminishing marginal utility, whereas the Log utility function in Question 2 implies that the consumer has constant marginal utility.

Question 3: To find the tax revenue the government collects, we need to find the consumer's demand for good 1 before and after the imposition of the quantity tax. First, we find the demand for good 1 before the imposition of the tax, using the same equation as in Question 2. Thus, in this case the demand for good 1 is e5. Therefore, the quantity consumed before the tax is e5.

Now, let’s find the consumer’s demand for good 1 after the imposition of the tax, which is equal to the consumer’s demand before the tax multiplied by (1 - t), with t = 0.2. Therefore, the demand for good 1 after the tax is 0.8e5.

Since the quantity tax of 0.2 is imposed on the consumer’s demand for good 1, the tax revenue is equal to 0.2 * 0.8e5 = 0.16e5.

Thus, the tax revenue the government collects from the consumer is 0.16e5.

Question 4: If the consumer has a preference over good 1 and good 2 represented by the utility function u(x₁, x₂) = x₁ + x₂, given the prices of good 1 and 2 are p₁ and p₂ respectively, and the consumer has a income of m, the demand for the two goods can be found using the following equation:

MRSxy = p₁/p₂

Therefore, for this problem we have MRS1,2 = p₁/p₂. Solving for the demands x₁ and x₂, we get:

x₁ = m/p₁, x₂ = m/p₂

Therefore, the demand for good 1 is m/p₁ and the demand for good 2 is m/p₂.

Therefore,

1) The demand for good 1 is 10/(5√2) and the demand for good 2 is 50√2/2.

2) The demand for good 1 is e5 and the demand for good 2 is e2.

3) The tax revenue the government collects from the consumer is 0.16e5.

4) The demand for good 1 is m/p₁ and the demand for good 2 is m/p₂.

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Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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The results using Fermat's little theorem are:

a. \(315 \mod 13 = 1\)

b. \(1518 \mod 17 = 1\)

c. \(4567 \mod 17 = 1\)

d. \(145102 \mod 101 = 1\)

Fermat's little theorem states that if p is a prime number and a is an integer not divisible by p, then \(a^{p-1} \equiv 1 \mod p\). We can use this theorem to find the results of the given congruences:

a. To find \(315 \mod 13\), we note that 13 is a prime number. Since 315 is not divisible by 13, we can apply Fermat's little theorem. We have \(315^{12} \equiv 1 \mod 13\). Simplifying this expression, we get \(315 \equiv 1 \mod 13\). Therefore, \(315 \mod 13 = 1\).

b. For \(1518 \mod 17\), we again use Fermat's little theorem. Since 17 is prime and 1518 is not divisible by 17, we have \(1518^{16} \equiv 1 \mod 17\). Simplifying this expression, we find \(1518 \equiv 1 \mod 17\). Hence, \(1518 \mod 17 = 1\).

c. Similarly, for \(4567 \mod 17\), we apply Fermat's little theorem. Since 17 is prime and 4567 is not divisible by 17, we have \(4567^{16} \equiv 1 \mod 17\). This simplifies to \(4567 \equiv 1 \mod 17\). Therefore, \(4567 \mod 17 = 1\).

d. Lastly, for \(145102 \mod 101\), we can once again use Fermat's little theorem. Since 101 is prime and 145102 is not divisible by 101, we have \(145102^{100} \equiv 1 \mod 101\). This simplifies to \(145102 \equiv 1 \mod 101\). Thus, \(145102 \mod 101 = 1\).

Therefore, the results using Fermat's little theorem are:

a. \(315 \mod 13 = 1\)

b. \(1518 \mod 17 = 1\)

c. \(4567 \mod 17 = 1\)

d. \(145102 \mod 101 = 1\)

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Answer: f⁻¹(x)=x/5

Step-by-step explanation:

To find the inverse function, you replace the y with x, and x with y.

x=5y

y=x/5

f⁻¹(x)=x/5

The curl and divergence of the given vector field can be determined by the following steps :

(a) The curl of the given vector field F(x, y, z) = 5eˣʸ sin(z)j + 4y tan⁻¹(x/z)k is:

curl F = ∇ × F = (∂F₃/∂y - ∂F₂/∂z)i + (∂F₁/∂z - ∂F₃/∂x)j + (∂F₂/∂x - ∂F₁/∂y)k.

Evaluating the partial derivatives, we have:

∂F₁/∂y = 5xeˣʸ sin(z),

∂F₂/∂z = 0,

∂F₃/∂x = 4y / (1 + (x/z)²),

∂F₃/∂y = 0,

∂F₁/∂z = 5eˣʸ cos(z),

∂F₂/∂x = 4y / (1 + (x/z)²).

Substituting these values into the curl equation, we get:

curl F = (0 - 0)i + (5xeˣʸ sin(z) - 4y / (1 + (x/z)²))j + (4y / (1 + (x/z)²) - 5eˣʸ cos(z))k.

(b) The divergence of the vector field F can be calculated as:

div F = ∇ · F = ∂F₁/∂x + ∂F₂/∂y + ∂F₃/∂z.

Evaluating the partial derivatives, we have:

∂F₁/∂x = 5yeˣʸ sin(z),

∂F₂/∂y = 0,

∂F₃/∂z = 5eˣʸ cos(z).

Substituting these values into the divergence equation, we get:

div F = 5yeˣʸ sin(z) + 0 + 5eˣʸ cos(z).

Therefore, the divergence of the vector field F is 5yeˣʸ sin(z) + 5eˣʸ cos(z).

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Answer:

15

Step-by-step explanation:

.

The greatest number of books by a student in this group is 15.

An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.

W can find the values of the upper and lower quartile and median from a box plot.

The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.

The formula used is Upper quartile - Lower quartile.

We have,

From the box plot,

We can see that,

Median = 6

First quartile = 2

Third quartile = 10

Smallest number = 2

Highest number = 15

Thus,

The greatest number of books by a student in this group is 15.

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A. A graph of the function y = -0.05x + 12 is shown on the coordinate plane below.

B. The domain and range of the part of the function graphed include:

Domain = [-40, 40].

Range = [10, 14].

In this scenario, we would use an online graphing calculator to plot the given linear function y = -0.05x + 12 in slope-intercept form for -40 ≤ x ≤ 40, as shown in the graph attached below.

Part B.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-40, 40] or -40 ≤ x ≤ 40.

Range = [10, 14] or 10 ≤ x ≤ 14.

When x = -40, the y-value (range) can be determined as follows;

y = -0.05x + 12

y = -0.05(-40) + 12

y = 2 + 12

y = 14.

When x = 40, the y-value (range) can be determined as follows;

y = -0.05x + 12

y = -0.05(40) + 12

y = -2 + 12

y = 10.

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Answer:

none

Step-by-step explanation:

because its an impossible.

Answer:

Domain is 3 <x>_-2

Range is 6 <x>_-3 (the lines are supposed to be under the >. it means equal to)

Step-by-step explanation:

First look on the x-axis, is goes from 3 to -2. now look at the colored in dot. that means more than or equal to. So the sign of -2 is x >_ -2. put the 3 on the other side. It stops at three so the sign is > 3. so 3<x>_ -2

Do the same with the y-axis except look up and down instead of left and right. so the numbers are 6 and -3. Use the same method above. this is set builder notation.

Answer:

4 x -2

Step-by-step explanation:

4 * -2 = -8

-24 / -3 = 8

11 + (-3) = 8

11 - (-3) = 14

Answer:

y-intercept = 3

Step-by-step explanation:

value that's on the y - axis

Answer:

width = 8 inches;     length = 28 inches

Step-by-step explanation:

Length = 4 + 3w

width = w

Area = lw

224 = (4 + 3w) w

224 = 4w + 3w²

0 = 3w² + 4w - 224

( 3w + 28   )( w - 8) = 0

3w + 28 =0 ;  w - 8 = 0

 3w = -28  ;    w = 8

 w = -28/3

  reject negative answer    So width = 8 and the length = 4 + 3w

                                                                                 length = 4 + 3(8) = 4 + 24

                                                                                Length = 28    

When you multiply a negative number by another negative number, the result is always a positive number.

This rule is based on the properties of multiplication and the concept of negative numbers.

When two negatives are multiplied, the negative signs "cancel out" each other. Mathematically, if you have -a multiplied by -b, where a and b are positive values, the result is given by ab.

For example, if you multiply -2 by -3, the product is 6, which is a positive number. This can be explained by the idea that multiplying two numbers with opposite signs results in a negative product, while multiplying two numbers with the same sign (both negative) produces a positive product.

Therefore, when you multiply a negative by a negative, the outcome is a positive number.

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