50 POINTS__ Solve for z and graph the solution.

–7 ≥ z–10 ≥ –14

Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it.

Answer:x+y=36

xy=256

x=256/y

256/y + y = 36

256/y + y²/y = 36y/y

y² - 36y +256 = 0

use the quadratic formula to get 18+2√17 and 18-2√17.

Step-by-step explanation:

The most appropriate choice for Green's Theorem, Cauchy Riemann Equation and Cauchy Goursat Theorem will be given by-

Cauchy Goursat Theorem has been proved using Green's Theorem-

What is Green's Theorem, Cauchy Riemann Equation and Cauchy Goursat Theorem?

Green's Theorem

Let C be a positively oriented, piecewise smooth, simple closed curve in a plane, and let D be the region bounded by C. Then

Green's Theorem states that

[tex]\int_c (Mdx + Ndy)=\int_D(M_x - N_y)dxdy[/tex]

M and N are functions of x and y

Cauchy Goursat Theorem

If a function f is analytic at all points interior to and on a simple closed contour C, then

[tex]\int_c f(z) dz = 0[/tex]

Cauchy Riemann Equation

If [tex]f(z)=u(x,y) + i v(x,y)[/tex] is analytic at z = x + iy then Cauchy Riemann Equation states that

[tex]u_x = v_y, u_y = -v_x[/tex]

Here,

Let [tex]f(z) = U(x,y) + iV(x,y)[/tex]

[tex]U, V, x, y[/tex] are continuous

[tex]f(z)dz = (U + i V)(dx + i dy)[/tex]

[tex]f(z) dz = (U dx - Vdy)+i(Vdx + Udy)[/tex]

[tex]\int_c f(z) dz = \int_c(U dx - Vdy)+i\int_c(Vdx + Udy)[/tex], C is the curve

By Green's Theorem,

[tex]\int_c f(z)dz = \int_D(U_ydydx - V_xdxdy)+i\int_D(U_xdxdy + V_ydydx)[/tex], D is the surface

[tex]\int_c f(z)dz = \int_D(-U_y - V_x)dxdy+i\int_D(U_x - V_y)dxdy[/tex][tex]\int_c f(z)dz = \int_D(V_x - V_x)dxdy+i\int_D(U_x - U_x)dxdy[/tex]

Since [tex]f'[/tex] is continuous, [tex]f[/tex] is analytic

So [tex]f[/tex] satisfies Cauchy Riemann equation

[tex]U_x = V_y, U_y = -V_x[/tex]

So,

[tex]\int_c f(z)dz = \int_D(V_x - V_x)dxdy+i\int_D(U_x - U_x)dxdy[/tex]

[tex]\int_c f(z)dz = 0[/tex]

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Complete Question

Suppose f is continuously complex differentiable on Ω , and T⊂Ω is a triangle whose interior is also contained in Ω . Apply Green's theorem to show that

[tex]\int_T[/tex] f(z)dz=0

This provides a proof of goursat’s theorem under the additional assumption that f′ is continuous.

.

Considering the numeric values of the function, we have that:

a) S(0) represents the remaining number of socks after 0 pairs are sold, and S(6) represents the remaining number of socks after 6 pairs are sold.

b) S(0) = 14, S(6) = 12.

c) The domain is not all real numbers, as the remaining number of socks cannot be negative, hence the domain is of 0 ≤ p ≤ 7.

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.

For this problem, the function is given as follows:

S(p) = 14 - 2p.

In which S(p) is the remaining number of socks after p socks are sold.

Then the numeric values are:

The domain of a function is the set that contains all possible input values of the function. The remaining number of socks cannot be negative, hence the domain is of 0 ≤ p ≤ 7, and the graph is given at the end of the answer.

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Answer:

n = 5

Step-by-step explanation:

Any 3-digit number to the base n will have its rightmost digit have a place value of n⁰, its next rightmost digit a place value of n¹ and the leftmost digit will have a place value of n²

This means 133can be represented as follows
n²     n¹     n⁰

1       3      3

The actual value in terms of a base of 10

= 3 x n⁰ + 3  x n¹   + 1 x n²

= 3 x 1 + 3 x n + 1 x n²      (n⁰ = 1 and n¹ = n)

= 3 + 3n + 1n²

Since we are given the information that 133ₙ = 43₁₀
3 + 3n + 1n²  = 43

subtract 3 from both sides
3n + 1n² = 40

Rewrite as

n² + 3n = 40

Factoring n on the left side=>
n(n + 3) = 40

If we look at the factors of 40:
1 x 40

2 x 20

4 x 10

5 x  8

5 and 8 satisfy the condition n(n + 3) = 40

So n = 5

The values are (4) The value of rise in temperature is 10 °C, (5) The new temperature is -10 °C (6) halfway between the two numbers in each pair is -2, 3, 1, -4; (7) The other temperature is 1°C.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold math Z.

Given that,

Tom’s greenhouse temperature is increasing

(4) The temperature is increased from -5 °C to 5 °C

The temperature is raised by 10 °C

(5) The temperature this morning was -6 °C. This afternoon, the

temperature dropped by 4 degrees

The new temperature is -10 °C

(6) The integer that

is halfway between the two numbers in each pair below.

a. 1 and -5 is -2

b. 5 and 1 is 3

c. -3 and 5 is 1

d. -3 and -5 is -4

(7) The difference between two temperatures is 3 degrees.

One temperature is 2°C.

The other temperature is 1°C.

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Answer: 11.78

Step-by-step explanation: So 11 would be your number before the decimal ( and stands for the decimal point ) then 78 would go after the decimal point.

Hope this helped!!!

Answer:

Q14 = 45

Q15 = 1.98

Step-by-step explanation:

Q14.

2t = 90 degrees (right angle)

(1) t = 45 (90 ÷ 2)

45 + 8 = 53

45 - 12 = 33

Q15.

43s = 85 degrees

s = 1.98 (85 ÷ 43)

Answer:

  8 cups

Step-by-step explanation:

Given a recipe for trail mix that calls for 1 cup of nuts for each 2 cups of granola, you want to know the number of cups of granola required for 12 cups of trail mix.

The fraction of the total volume of trail mix that is granola is ...

  granola / (trail mix) = granola / (nuts + granola)

  (2 cups)/(1 cup +2 cups) = 2/3

Applied to the quantity 12 cups of trail mix, we find the volume of granola to be ...

  granola = (2/3)×(12 cups) = 8 cups

You need 8 cups of granola for 12 cups of trail mix.

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An angle of rotation is the measure of the amount that a figure is rotated about a fixed point called a point of rotation.

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Answer:

.- El complemento de un ángulo nulo es el ángulo recto. 2.- El complemento de un ángulo recto es un ángulo nulo. 3.- El suplemento de un ángulo recto es otro ángulo recto. 4.- El suplemento de un ángulo obtuso sería lo que le falta para llegar a 180.

Step-by-step explanation:.- El complemento de un ángulo nulo es el ángulo recto. 2.- El complemento de un ángulo recto es un ángulo nulo. 3.- El suplemento de un ángulo recto es otro ángulo recto. 4.- El suplemento de un ángulo obtuso sería lo que le falta para llegar a 180.

The probability that at least one electrical components does not function properly is 83.3%

To make the calculation easier, use the following property:

P(at the very least one) = 1 - P (None)

The total number of electrical components is 6.

Number that which not work well: 1

Number that works well: 5

We have options for selecting 4 good components from a set of 5 by;

⁵C₄  = 5

We have 4 options from a total of 6 components by;

⁶C₄ = 6

We have a way to do this if everything works properly; ¹C₀ = 1

P(at the very least one) = ⁵C₄× ¹C₀ /⁶C₄

P(at the very least one) = 5 / 6

P(at least one) = 0.833 = 83.3%

Thus, the probability that at least one of the electrical component will not function is 83.3%.

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The number of randomly selected Americans that must be surveyed is equal to 38 if the confidence interval is 97.5% with a 0.16 margin of error.

First, we calculate the critical value as follows;

a = (1 - 0.975) = 0.025 = 0.025 / 2 = 0.0125 = (1 - 0.0125) = 0.9875

Z - Critical value = NORM.S.INV (0.9875) = 1.96

As margin of error(ME) = 0.16

Therefore;

n = pq(Z²) / ME²

n = 0.5 × 0.5 (1.96)² / (0.16)²

n = 0.25 × 3.8416 / 0.0256

n = 0.9604 / 0.0256

n = 37.515

Rounding it to the nearest whole number;

n = 37.515 = 38

Hence 38 randomly selected Americans must be surveyed if the estimated confidence interval is 97.5% and the margin of error is 0.16.

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Answer:

see explanation

Step-by-step explanation:

a

the error she has made is in cancelling the values in the denominators.

When cancelling fractions, this is performed between values on the numerator with values on the denominator.

correct result is

[tex]\frac{1}{15}[/tex] × [tex]\frac{3}{5}[/tex] ( cancel the 3 and 15 by 3 )

= [tex]\frac{1}{5}[/tex] × [tex]\frac{1}{5}[/tex]

= [tex]\frac{1}{25}[/tex]

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

b

as an estimate, multiply the numerators and denominators, that is

[tex]\frac{1(3)}{15(5)}[/tex] = [tex]\frac{3}{75}[/tex] = [tex]\frac{1}{25}[/tex]

Answer:

(-3/4, 0) and (0, 3/2)

Step-by-step explanation:

The [tex]x[/tex]-intercept is when [tex]y=0[/tex].

[tex]\frac{3}{4}+x=0 \implies x=-3/4[/tex]

So, the [tex]x[/tex] intercept has coordinates [tex](-3/4, 0)[/tex].

The [tex]y[/tex] intercept is when [tex]x=0[/tex].

[tex]\frac{3}{4}=\frac{1}{2}y \implies y=3/2[/tex].

So, the [tex]y[/tex] intercept has coordinates [tex](0, 3/2)[/tex]

The computation shows that 1756.18595945 to the nearest hundred-thousandth will be 1756.18596.

After being rounded, the value of the hundred thousandth place, which is five places to the right of the decimal point, determines the value of the nearest ten thousandth of a decimal number, which is the value four places to the right of the decimal point.

The thousandth digit should be rounded down if the digit is less than 5. If that number is five or more, round it up to the nearest thousand. We must round up the thousandth digit because in the example given above, the digit following the thousandth digit (i.e., 9) is more than 5. This will give a value of 1756.18596.

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The solution for the given inequality is :

x < -19

In interval notation it is:

(-∞, -19)

And the graph can be seen in the image below-

Here we have the following inequality:

7*(2x + 5) < 3*(4x - 1)

To solve it, we need to isolate x in one of the sides of the inequality. Doing that we will get:

14x + 35 < 12x - 3

14x - 12x < -3 - 35

2x < - 38

x < -38/2

x < -19

This is the solution, written in interval form it is:

(-∞, -19)

And to graph this, we need to graph an open dot at x = -19 (which means that x = -19 is not a solution) and a line that goes to the left, it will be something like in the image below.

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Differences with in number of volunteers can explain  60.01% of the variation in the amount of trash bags collected.

The coefficient of correlation (r) between both the number of volunteers x and also the number of trash bags collected y is 0.775.

To calculate the percentage of variation for one derivative contract by the other, simply square the correlation coefficient.

Here, r = 0.775

Squaring both side.

r² = 0.775²

r² = 0.600625

Simply multiply with 100 to get the percent.

r² = 60.0625

r² = 60.01

Thus, differences in the number of volunteers can explain 60.01% of the variation in the number of trash bags collected.

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When Jerry puts 1500 pounds in the bank for 5 years then the rate of interest which makes the amount equal for Jerry and Neil is 1.85%.

Given Neil puts 1550 pounds in the bank, at a rate of 3% compound interest.

we need to calculate the total amount and interest at the end of 5 years.

P=1500 pounds

r = 3%

n = 5 years.

A = P(1+r/100)ⁿ

A = 1500(1+3/100)⁵

A = 1500(103/100)⁵

A = 1500 × 103/100 × 103/100 × 103/100

A = 3278181/2000

A = 1639.09

C.I = A-P

= 1639.09 - 1500

= 139.09

From the question, After 5 years they have the same amount.

Therefore we use the amount to calculate rate of interest as :

A = 1639.09

Simple interest = 1639.09 - 1500

= 139.09

Therefore, P = 1500

I = 139.09

t = 5 yrs

R = (100×I)/(P×t)

R = (100×139.09)/(1500×5)

R = 1.85%

Hence the rate of interest is 1.85%.

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Based on the amount of water in the tub that Archimedes is draining as a function of time, the rate that the water drains is A. 72 liters per minute

The speed that the water drained is the same as the slope of the line. That slope can be found by the formula:

= Change in y / Change in x

Pick two points from the line;

(0, 360) and (5, 0)

The slope is:
= (0 - 360) / (5 - 0)

= -360 / 5

= - 72

This means that every minute, Archimedes  would have drained the water by 72 liters.

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The number of carrots and potatoes that Mark will need for 3 servings will be 6 carrots and 3 potatoes.

It should be noted that an expression is simply used to show the relationship between the variables that are illustrated.

From the information, Mark's soup recipe makes 10 servings and uses 4 carrots and 2 potatoes. Therefore, to make 5 servings, he will need half of the carrots and potatoes. This will be 2 carrots and 1 potatoe.

Therefore, to make 15 servings, the total needed will be;

= (4 + 2 carrots) as (2 + 1 potatoes)

= 6 carrots and 3 potatoes

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Circle A and Circle B's connection

Circle A's size is more significant than Circle B's size.

As a result, circle A's radius exceeds circle B's radius.

The connection between segments

1.

Let M be the location where Segment QT and ER intersect.

Additionally, tangents from an outside point to a circle have identical lengths.

QM = ME———— (1)

MT=MR————(2)

Including (1) and (2)

MR + ME = QM + MT

Q T=ER

2.

Tangents from an exterior point to a circle have identical lengths.

We may write the following segments are equal using this property.

UP=U Q

Z C=ZR

V C=VS

NR=NS

KC=K T

What are Tangents?

A line that only touches a circle or an ellipse at one point is said to be divergent in geometry. If a line contacts a curve at point P, that point is referred to as the point of tangency. In other words, it is described as the line that, at that particular location, indicates the slope of a curve. The following methods can be used to find the tangent equation in differential geometry:

As we are aware, the gradient of the curve at any given location on the curve is equal to the gradient of the tangent to the curve. The following is how to determine the tangent equation of the curve y = f(x):

Utilizing the differentiation principles, determine the gradient function's derivative.

To determine the tangent's gradient, the derivative should be changed to include the provided point's x-coordinate

Find the tangent equation by substituting the provided coordinate point and the gradient of the tangent into the straight-line equation (in a slope-point formula).

Circle's Tangent

A closed, two-dimensional form, a circle is also a curve. The radius of the circle or the line from the center O to the point of tangency is always vertical or perpendicular to the tangent line AB at P, i.e., OP is perpendicular to AB as illustrated in the accompanying picture.

Geometric Tangent

Here, "AB" stands for the tangent, "P" for the point of tangency, and "O" for the circle's center. The OP is the radius of the circle.

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Answer:

2/5--1/4=3

Step-by-step explanation:

lcm is 20 =8-5=3/20=3 =20

Answer:

Car C  with a gas mileage of 18.18 mpg

Step-by-step explanation:

Compute mileages by the formula: Miles Driven/Gas Consumed and choose the highest value

Car A:  500 /  33.4 = 14.97 mpg

Car B : 43 / 2.5  = 17.2 mpg

Car C: 100 / 5.5 = 18.18 mpg

If a football team gained [tex]2\frac{3}{4}[/tex] yards and then lost [tex]4\frac{3}{5}[/tex] yards on the next play, then their total loss is  [tex]1\frac{17}{20}[/tex] yards

The total yards they gained in first match =  [tex]2\frac{3}{4}[/tex] yards

Convert the mixed fraction to the simple fraction

[tex]2\frac{3}{4}[/tex] yards = 11/4 yards

The total yards they loss in second match = [tex]4\frac{3}{5}[/tex] yards

Convert the mixed fraction to the simple fraction

[tex]4\frac{3}{5}[/tex] yards = 23/5 yards

Total loss = The total yards they loss in second match- The total yards they gained in first match

Substitute the values in the equation

Total loss = 23/5 - 11/4

= 37/20 yards

Convert the simple fraction to the mixed fraction

37/20 yards = [tex]1\frac{17}{20}[/tex] yards

Hence, If a football team gained [tex]2\frac{3}{4}[/tex] yards and then lost [tex]4\frac{3}{5}[/tex] yards on the next play, then their total loss is  [tex]1\frac{17}{20}[/tex] yards

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Answer:

Step-by-step explanation:

Answer:

48484

Step-by-step explanation:

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