Need help on these 2 questions please??? 14 points ?

Answer:

56π

Step-by-step explanation:

1. Approach

To find the radius of a circle, use the formula;

\(A = r^{2}\)π

To find the area of the shaded region, find the area of the larger circle, and then subtract the area of the smaller circle from it.

It is given that the larger circle has a radius of 9, and the smaller has a radius of 5.

2. Area of the larger circle

\(A = r^{2}\)π

Substitute in known value (use 3.14 for π)

\(A = (9)^{2} * 3.14\)

A = 254.47

3. Area of the smaller circle

\(A = r^{2}\)π

Substitute in known value (use 3.14 for π)

\(A = (5)^{2} * 3.14\)

A = 78.54

4. Area of the shaded region

Subtract the area of the smaller circle from the area of the larger circle;

254.47 - 78.54 = 175.93

~ 56π

Answer:

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

We have a repeating decimal 4.6(1).

Let's express it as a GP:

Fund the sum of infinite GP, with the first term of a = 0.01 and common ratio of r = 0.1:

Add 4.6 to the sum:

Hence the fraction is 4 11/18.

Answer:

ima say around 5 and 1/4 cups

Step-by-step explanation:

3 1/2 divided by 2/3 cand be round to

3 3/6 divided by 4/6 to make it easier

Answer: E. 5 1/4

Step-by-step explanation:

Answer:

2560000 or 2.56*10^6

Step-by-step explanation:

\(\frac{((-4)^6)^2*(-5^2)^3}{(-4)^6*(-5)^2}\)

\(\frac{(-4)^1^2*(-5^6)}{(-4)^6*(-5)^2}\)

\(\frac{16777216*15625}{4096*25}\)

\(\frac{262144000000}{102400}\)

\(2560000\)

Answer:

\(-2(3x - 4) = -16\) and \(20- 15x = 6 - 2(4x + 7)\)

Step-by-step explanation:

Given

\(-2(3x - 4) = -16\)

\(\frac{1}{2}(10x + 2) = 6\)

\(20- 15x = 6 - 2(4x + 7)\)

\(\frac{1}{3}(9x - 12) + 6=-10\)

Required

Equations with \(x = 4\) as a solution

\(-2(3x - 4) = -16\)

Divide both sides by -2

\(3x - 4 = 8\)

Add 4 to both sides

\(3x - 4 +4= 8+4\)

\(3x =12\)

Divide both sides by 3

\(x = 4\)

\(\frac{1}{2}(10x + 2) = 6\)

Multiply both sides by 2

\(10x + 2 = 12\)

Subtract 2 from both sides

\(10x + 2 -2= 12-2\)

\(10x = 10\)

Divide both sides by 1

\(x = 1\)

\(20- 15x = 6 - 2(4x + 7)\)

Open bracket

\(20 - 15x = 6 - 8x - 14\)

Collect like terms

\(8x - 15x = 6 - 14 - 20\)

\(-7x = -28\)

Divide both sides by -7

\(x = 4\)

\(\frac{1}{3}(9x - 12) + 6=-10\)

Subtract 6 from both sides

\(\frac{1}{3}(9x - 12) + 6-6=-10-6\)

\(\frac{1}{3}(9x - 12) =-16\)

Multiply both sides by 3

\(9x - 12 = -48\)

Add 12 to both sides

\(9x - 12 +12= -48+12\)

\(9x = -36\)

Divide both sides by 4

\(x =-4\)

\(-2(3x - 4) = -16\) and \(20- 15x = 6 - 2(4x + 7)\) have \(x = 4\) has a solution

Answer: 1st and 3rd

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

answer is 7

Unicode value of 66, which is the letter "B". Therefore, the correct answer to this question is option B: "B".

The terms you mentioned are related to the Unicode character encoding standard and the concept of evaluating expressions. When discussing the expression "A" + 1, it's essential to note that the Unicode value for the character "A" is 65.

The expression "A" + 1 is attempting to add a numerical value (1) to a character ("A"). In many programming languages, this operation is allowed, and the result would be based on the Unicode values of the characters involved. Since the Unicode value for "A" is 65, adding 1 to it would result in a new Unicode value of 66. Consequently, the evaluated expression would correspond to the character with the Unicode value of 66, which is the letter "B". Therefore, the correct answer to this question is option B: "B".

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a) No, p1 = 20, p2 = 19.50 is not a Nash Equilibrium.

b) Yes, there is a Nash Equilibrium in which Firm 2 makes a positive profit.

c) Player 1 has infinitely many strategies.

d) Yes, p1 = 15, p2 = 15 is a Nash Equilibrium.

e) No, p1 = 21, p2 = 21 is not a Nash Equilibrium.

Nash Equilibrium is a state of a strategic game where no player has an incentive to deviate from his or her chosen strategy after considering the strategies of other players. A game has more than one Nash equilibrium if players are unable to agree on a cooperative strategy to play.

Finding Nash Equilibrium

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Answer:

112 degrees

Step-by-step explanation:

In this case, the two angles are considered alternating exterior angles, which signifies that they are equal

2x-6y= 36-4x is the equations create a system of equations with no solution.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign.

When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

Hence, 2x-6y= 36-4x is the equations create a system of equations with no solution.

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Answer:

No

Step-by-step explanation:

Because the number 4 repeats itself in a function no numbers repeat themselves

The 99% confidence interval for the mean score of all students is constructed as (85.497, 96.5026).

Given,

Sample size, n = 30

Sample mean, x = 91

Standard deviation, s = 11.7

The 99% confidence interval for the mean score of all students can be calculated as,

x ± z \(\frac{s}{\sqrt{n} }\)

z value for 99% confidence interval = 2.576

Confidence interval = (91 ± (2.576 × 11.7/√30)

                                 = (91 ± 5.5026)

                                 = (85.497, 96.5026)

Hence the confidence interval is (85.497, 96.5026).

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Answer: a. b. and c.

Step-by-step explanation:

a.- (f)1=14 is correct in this explanation because 15-

1=14

b.- f(2)=15 is incorrect. 15-2 does not equal 15. It would be 13.

=0

c.- f(12)=3 is correct because 15-12=3

d.- f(15)=0 is correct because 15-5=

The domain of a function is the set of all input values (x-values) for which the function produces a valid output (y-value). In this case, the function f(x) = (x+2)(x+6) is defined for all real numbers, so the domain is all real numbers.

What do a function example's range and domain mean?

A straightforward function, such as f(x) = x2, can have a domain (what goes in) of just the counting numbers 1, 2, 3, etc., and a range (what comes out) of the set 1, 4, 9, etc. Another function, g(x) = x2, may have an integer domain of..., -3, -2, -1, 0... 1, 2, 3, and its range is..., 1, 4, 9,...

The range of a function is the set of all possible output values (y-values) produced by the function. The function f(x) = (x+2)(x+6) is a polynomial, and all polynomials of the form (ax^2 + bx + c) with real coefficients (a,b,c) have range is all real numbers. The range of the function f(x) = (x+2)(x+6) is also all real numbers.

So the answer is

The domain is all real numbers, and the range is all

real numbers.

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Answer:

No. pp you can fit in a van: 6,

No. pp you can fit in a bus: 20

Step-by-step explanation:

Let v = # of pp in vans, and let b = # of pp in buses:

8v + 9b = 228,

4v + 5b = 124

If we solve this system of equations by substitution, we isolate the first eq. for v and then substitute into the bottom eq:

v = 228-9b/8,

Substitute v = 228-9b/8 into bottom eq:

[4 * 228-9b/8 + 5b = 125]

[228+b/2=124]

[228+b = 248]

[b = 20]

Now substitute 20 to find no. of pp in the vans:

v = 228 - 9(20)/8 = 228  - 180/8 = 48/8 = 6

Step-by-step explanation:

vol of sphere =

\((4 \div 3) \times {5}^{3} \times \pi\)

523.59 units^3

Answer:

523.33 units³

Explanation:

Volume of a sphere = \(\frac{4}{3}\)πr³ - Here the radius is 5 and take π as 3.14.

Using the formula:

If the probability that interest rates will go up and house sales will decrease is estimated to be 0.15, the probability of an increase in interest rates and not a decrease in house sales is 0.05.

To find the probability of an increase in interest rates and not a decrease in house sales, we can use the formula for conditional probability:

P(Interest rates increase and house sales don't decrease) = P(Interest rates increase) - P(Interest rates increase and house sales decrease)

We are given that the probability of interest rates on housing loans going up in the next 6 months is 0.20, and the probability of house sales decreasing is 0.6. We are also given that the probability of interest rates going up and house sales decreasing is 0.15.

To find the probability of interest rates going up and not house sales decreasing, we subtract the probability of interest rates going up and house sales decreasing from the probability of interest rates going up:

P(Interest rates increase and house sales don't decrease) = 0.20 - 0.15 = 0.05

In summary, we can use conditional probability to calculate the probability of an increase in interest rates and not a decrease in house sales.

Given the probabilities of interest rates going up and house sales decreasing, we can subtract the probability of interest rates going up and house sales decreasing from the probability of interest rates going up to find the probability of interest rates going up and not house sales decreasing.

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Answer:

The correct option is;

B. s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t

Step-by-step explanation:

The given parameters are;

The number of T-shirts, t, and shorts, s, Tim must design a day = 12

The maximum number of T-shirts and shorts Tim can design a day = 30

The maximum number of hours Tim can work = 18 hours

Therefore, we have;

The number of shorts Tim designs in a day is ≥ The minimum number of T-shirts and shorts Tim must design a day less the number of T-shirts Tim designs

Which gives;

s ≥ 12 - t

Also the number of shorts Tim designs in a day is ≤ The maximum number of T-shirts, and shorts, Tim can design a day less the number of T-shirts Tim designs

Which gives;

s ≤ 30 - t

The number of 45 minute period for the design of shorts in 18 hours = 18×60/45 = 24

The fraction of 36 minutes in 45 minutes = 36/45 = 0.667

Therefore we have;

The number of shorts Tim designs in a day is ≤ The number of 45 minute periods in 18 hours less the number of 36 minutes periods used to design T-shirts

Which gives;

s ≤ 24 - 0.66·t

The correct option is s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t.

Answer:

B. s> 12-tss 30 - t Ss 24 -0.66t, s 2 0; t> 0

Step-by-step explanation:

Hope this helps!!

if f(x, y) = xy, find the gradient vector ∇f(3, 7) and use it to find the tangent line to the level curve f(x, y) = 21 at the point (3, 7): This is the equation of the tangent line to the level curve f(x, y) = 21 at the point (3, 7).

To find the gradient vector ∇f(3, 7) for the function f(x, y) = xy, we first need to compute the partial derivatives of f with respect to x and y:

∂f/∂x = y
∂f/∂y = x

Therefore, the gradient vector ∇f is given by:

∇f = (∂f/∂x, ∂f/∂y) = (y, x)

Evaluating ∇f at the point (3, 7), we get:

∇f(3, 7) = (7, 3)

This is the gradient vector at the point (3, 7) on the level curve f(x, y) = 21.

To find the tangent line to the level curve at (3, 7), we can use the fact that the gradient vector ∇f is orthogonal to the level curve at each point. In other words, the tangent line at (3, 7) is perpendicular to the vector (7, 3).

Recall that the equation of a line in two dimensions can be written as:

y - y_0 = m(x - x_0)

where m is the slope of the line and (x_0, y_0) is a point on the line.

To find the slope of the tangent line at (3, 7), we can use the fact that it is perpendicular to the gradient vector ∇f(3, 7). The dot product of two orthogonal vectors is zero, so we have:

(7, 3) · (x - 3, y - 7) = 0

Expanding the dot product and solving for y, we get:

7(x - 3) + 3(y - 7) = 0
y - 7 = (-7/3)(x - 3)

This is the equation of the tangent line to the level curve f(x, y) = 21 at the point (3, 7).

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In the given word problem, the rate of change is the change in the cost of the ice cream concerning the change in the number of scoops.

That is, the rate of change is the ratio of the change in the cost of ice cream and the change in the number of scoops. Let's first calculate the initial rate of change or slope of the given deal: When we buy a waffle cone, the cost is $3, and we can buy one scoop of ice cream for $1.50.So, for one scoop of ice cream, the total cost would be 3 + 1.50 = $4.50.

We can represent the cost of one scoop of ice cream with the help of a linear equation: y = mx + b. Here, the slope or the rate of change, m = Change in cost of ice cream/ Change in the number of scoops= 1.5/1= 1.5Therefore, the rate of change of the ice cream with respect to the number of scoops is $1.50/scoop.

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\(\quad \qquad \huge \bf \dag \: Answer \: \dag\)

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\( \underline{ \large \rm Solution} : \)

\(\rm Given : \)

Two equations are -

\( \rm Procedure : \)

Considering the equations as (i) and (ii) respectively

From equation (i) -

put this value of y in equation (ii) -

Next thing to do would be to put value of x we got in equation (i) to get y

Values asked are :

\( \rightarrow \rm y = - 4\)

\( \rightarrow \rm x= - 2\)

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\( \large \bf hope \: \: it \: \: helps \: - dabI \)

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Answer:

  (b)  y -4 = 3(x -2)

Step-by-step explanation:

You are given the form

  y -y1 = m(x -x1)

and the values

  y1 =4, m =3, x1 =2

Putting these in their places gives ...

  y -4 = 3(x -2)

Answer:

\(5\times10^3\)

Step-by-step explanation:

\(3.55\times10^6 \div 7.1 \times 10^2\)

Exponents are positive:

\(3.5.5.0.0.0.0. = 3550000\)

\(7.1.0.=710\)

\(3550000 \div 710 = 5000\)

Convert back into scientific notation:

\(5000 = 5 \times 10^3\)

\(= 5 \times10^3\)

Hope this helps.

Answer: 5 x 10^3

Step-by-step explanation:

If the best fit line is nearly horizontal, it suggests no significant relationship between height and head circumference.

In this scenario, the explanatory variable is the child's height, as it is being used to predict the head circumference.

The response variable is the head circumference itself, as it is the variable being predicted or explained by the height.

To draw a scatter diagram of the data, you would plot the child's height on the x-axis and the corresponding head circumference on the y-axis. Each data point would represent a child's measurement pair.

Once all the data points are plotted, you can then draw the best fit line, also known as the regression line, that represents the overall trend or relationship between height and head circumference.

By observing the scatter diagram and the best fit line, you can determine the relationship between a child's height and head circumference.

If the best fit line has a positive slope, it indicates a positive relationship, meaning that as height increases, head circumference tends to increase as well.

If the best fit line has a negative slope, it indicates a negative relationship, meaning that as height increases, head circumference tends to decrease.

By assessing the slope of the best fit line in the scatter diagram, you can determine whether the relationship between height and head circumference is positive, negative, or nonexistent.

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The numbering system we commonly use is called the decimal numbering system because it uses 10 symbols to represent all possible numbers.

A way of writing numbers is known as a number system.

There are the following number systems:

Hence, we can say that the numbering system we commonly use is called the decimal numbering system because it uses 10 symbols to represent all possible numbers.

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a) "You will get an A in this course if and only if you learn how to solve discrete mathematics problems."
b) "You will be informed if and only if you read the newspaper every day."
c) "It will rain if and only if it is a weekend day."
d) "You can see the wizard if and only if the wizard is not in."
e) "My airplane flight will be late if and only if I have to catch a connecting flight."

These propositions are written in the form "p if and only if q" in English, which means that both p and q must be true for the entire statement to be true.

This form is also known as a biconditional statement, and it is often used in logic and mathematics to express the relationship between two propositions.

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The standard deviation of the data-set is given as follows:

s = 4.14.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The data-set in this problem is given as follows:

3, 4, 5, 7, 10, 12, 15.

Hence the mean is:

Mean = (3 + 4 + 5 + 7 + 10 + 12 + 15)/7

Mean = 8.

The sum of the differences squared for the data-set is given as follows:

SS = (3 - 8)² + (4 - 8)² + (5 - 8)² + (7 - 8)² + (10 - 8)² + (12 - 8)² + (15 - 8)²

SS = 120.

The standard deviation is given by the square root of the sum of the differences squared divided by the cardinality, hence:

s = sqrt(120/7)

s = 4.14.

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The centre line of a control chart is calculated by computing the average (mean) of the data for every period.

In control chart analysis, the centre line represents the central tendency or average value of the process being monitored. It is typically obtained by calculating the mean of the data points collected over a specific period. The purpose of the centre line is to provide a reference point against which the process performance can be compared. Any data points falling within acceptable limits around the centre line indicate that the process is stable and under control.

The calculation of the centre line involves summing up the values of the data points and dividing it by the number of data points. This average is then plotted on the control chart as the centre line. By monitoring subsequent data points and their distance from the centre line, deviations and trends in the process can be identified. Deviations beyond the control limits may indicate special causes of variation that require investigation and corrective action. Therefore, the centre line is a critical element in control chart analysis for understanding the baseline performance of a process and detecting any shifts or changes over time.

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Christina's initial monthly cell phone bill is $50 and it increases at a rate of 0.02 dollars per month.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (60 - 50)/(500 - 0)

Slope (m) = 10/500

Slope (m) = 0.02

At data point (0, 50), a linear equation in slope-intercept form for this line can be calculated as follows:

y = mx + c

y = 0.02x + 50

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