what number is halfway between 86 and 102

The loss on selling 50 shares of stock would be 87.50.

To calculate the loss on selling 50 shares of stock originally bought at

\(13\frac{3}{4}\) and sold at 12, we need to determine the difference between the purchase price and the selling price, and then multiply it by the number of shares sold.

First, let's convert the purchase price from a mixed fraction to a decimal. \(13\frac{3}{4}\) can be expressed as 13.75.

Next, we calculate the difference between the purchase price and the selling price:

\(13.75 - 12 = 1.75.\)

Finally, we multiply the difference by the number of shares sold:

\(1.75 \times50 = 87.50.\)

Therefore, the loss on selling 50 shares of stock would be 87.50.

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Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Answer:

\(y = -\frac{2}{5}x + \frac{14}{5}\)

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

\(y = mx + c\)

In which m is the slope and c is the y-intercept(value of y when x = 0).

A(2;2) and B(-3;4)

When we have two points, the slope is the change in y divided by the change in x. So

Change in y: 4 - 2 = 2

Change in x: -3 - 2 = -5

Slope: \(m = \frac{2}{-5} = -\frac{2}{5}\)

So

\(y = -\frac{2}{5}x + c\)

A(2;2)

When \(x = 2, y = 2\). We use this to find c.

\(y = -\frac{2}{5}x + c\)

\(2 = -\frac{2}{5}(2) + c\)

\(c = 2 + \frac{4}{5} = \frac{10}{5} + \frac{4}{5} = \frac{14}{5}\)

So

\(y = -\frac{2}{5}x + \frac{14}{5}\)

Descartes must be thinking of the number 0.

Now, Let's call the number Descartes is thinking of "x".

Hence, According to the problem, if Descartes multiplies "x" by 9, he gets "x" back. In other words, 9 times "x" is equal to "x".

So we can write this as an equation:

⇒ 9x = x

Now we need to solve for "x". We can start by subtracting "x" from both sides of the equation:

⇒ 9x - x = 0

⇒ 8x = 0

divide both sides by 8 to get:

⇒ x = 0

Thus,  Descartes must be thinking of the number 0.

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Answer:

a) 265 case

b) 4 bottles

Step-by-step explanation:

The number of bottles remaining = total number of bottles - total number of bottles placed in cases

The number of bottles remaining = 8500 - 2136

The number of bottles remaining = 6364 bottles

From the table, we can see that water is filled at 24 bottles per case. Let x be the number of cases, hence:

24 bottles  per case * x case = 6364 bottles

24x = 6364

x = 6364

x = 265.16

Therefore the number of cases filled = 265.

265 cases can contain 6360 bottles

b) number of bottles remaining = 6364 bottles - (24 * 265 case) = 4 bottles

well, putting the movie in fifths, she watched 3/5, the whole movie will be 5/5 = 1.

\(\begin{array}{ccll} \stackrel{movie}{fraction}&hour\\ \cline{1-2} \frac{3}{5}&\frac{5}{8}\\[1em] \underset{whole}{1}&x \end{array}\implies \cfrac{~~ \frac{3}{5}~~}{1}=\cfrac{~~ \frac{5}{8}~~}{x}\implies \cfrac{3}{5}x=\cfrac{5}{8}\implies \cfrac{3x}{5}=\cfrac{5}{8} \\\\\\ 24x=25\implies x = \cfrac{25}{24}\implies x = 1\frac{1}{24}\qquad \textit{1 hour, 2 minutes and 30 seconds}\)

Answer:

(-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52

Step-by-step explanation:

i literally just learned this today so here we go:

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

We are given the center of the circle as (-7, -4), so we can substitute these values for h and k:

(x - (-7))^2 + (y - (-4))^2 = r^2

(x + 7)^2 + (y + 4)^2 = r^2

We also know that the circle contains the point (-1, -8).

We can substitute these values for x and y, and solve for r:

(-1 + 7)^2 + (-8 + 4)^2 = r^2

36 + 16 = r^2

r^2 = 52

Substituting this value of r^2 into the equation for the circle, we get:

(x + 7)^2 + (y + 4)^2 = 52

Therefore, the equation of the circle with center (-7, -4) containing the point (-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52

Answer:

It's option B, (f • g)(x) = 3x^3 + 6x^2 - 5x - 10

Step-by-step explanation:

In this problem, we are dealing with a branch of functions called composite functions. What the difference is between normal and composite functions is that we instead of defining a value for f(x), take two functions, f(x) and g(x), in the form of f and g. For instance, h(x) = g.

• Take the products of both functions.

f(x)g(x) = 3x²+5 • x-2

• Next, expand the functions. We expand by combining like terms.

= 3x^3 - 6x^2 + 5x - 10

Since the function cannot be simplified further, this leads to option B being our answer.

Hope this helps!

The area of right triangle is \(\frac{1}{15}\).

The given coordinates are \((-2,-1), (1, 1), (3,-2)\).

We have to find the area of right triangle.

To find the area we first draw the graph using that coordinate.

The graph of the coordinate is

To find the area we use the formula

\(\angle ABC=\frac{1}{2}(|AB|)(|AC|)\)

We first find the value of \((|AB|)\) and \((|AC|)\).

e coordinate of \(A\) is \((-2,-1)\) and \(B\) is \((1,1)\).

The slope of \((|AB|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

The slope of \((|AB|)=\frac{1-(-1)}{1-(-2)}\)

The slope of \((|AB|)=\frac{1+1}{1+2}\)

The slope of \((|AB|)=\frac{2}{3}\)

The coordinate of \(A\) is \((-2,-1)\) and \(C\) is \((3,-2)\).

The slope of \((|AC|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

The slope of \((|AC|)=\frac{(-2)-(-1)}{3-(-2)}\)

The slope of \((|AC|)=\frac{-2+1}{3+2}\)

The slope of \((|AC|)=-\frac{1}{5}\)

Now finding the area of right triangle by putting the values.

\(\angle ABC=\frac{1}{2}\times\frac{2}{3} \times(-\frac{1}{5})\)

Area can't be negative so

\(\angle ABC=\frac{1}{2}\times\frac{2}{3} \times\frac{1}{5}\\\angle ABC=\frac{2}{30}\\\angle ABC=\frac{1}{15}\)

Hence, the area of right triangle is \(\frac{1}{15}\).

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Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Answer:

all of them

Step-by-step explanation: Because the age bracket id between 56 and 59.

The probability is closer to one than zero.

Probability theory is used to analyze and predict the likelihood of events happening in various fields such as statistics, gambling, physics, finance, and more. It allows us to make informed decisions based on the likelihood of different outcomes. In probability theory, the total number of possible outcomes is important to determine the probability of a single event occurring. By comparing the favorable outcomes to the total outcomes, we can calculate the probability of an event happening.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Probability for Class 10 is an important topic for the students which explains all the basic concepts of this topic. The probability of all the events in a sample space adds up to 1.For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible (H, T). But when two coins are tossed then there will be four possible outcomes,  i.e {(H, H), (H, T), (T, H), (T, T)}.

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Answer:

\(\displaystyle \lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} = \boxed{ \frac{34}{23} }\)

General Formulas and Concepts:
Calculus

Limits

Limit Rule [Variable Direct Substitution]:
\(\displaystyle \lim_{x \to c} x = c\)

Limit Property [Multiplied Constant]:
\(\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)\)

Limit Property [Multiplication]:
\(\displaystyle \lim_{x \to c} f(x)g(x) = \lim_{x \to c} f(x) \lim_{x \to c} g(x)\)

Step-by-step explanation:

*Note:

The problem is too big to fit all work. I will assume that you know how to do basic algebra and calculus.

Step 1: Define

Identify given limit.

\(\displaystyle \lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}}\)

Step 2: Find Limit (Algebriaclly)

Rationalize the function and apply basic limit techniques listed under "Calculus":

\(\displaystyle\begin{aligned}\lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} & = \lim_{x \to 2} - \frac{17(x - 2)}{\big( \sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5} \big) \big( \sqrt{x + 7} + 3 \sqrt{2x - 3} \big)} \\& = -17 \lim_{x \to 2} \frac{1}{\sqrt{x + 7} + 3 \sqrt{2x - 3}} \lim_{x \to 2} \frac{x - 2}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}}\end{aligned}\)

\(\displaystyle\begin{aligned}\lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} & = - \frac{17}{6} \lim_{x \to 2} \frac{x - 2}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} \\\end{aligned}\)

Let's now focus on just the rationalization of the function within the limit:

\(\displaystyle\begin{aligned}\frac{x - 2}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} & = \frac{(x - 2) \bigg[ (x + 6)^\Big{\frac{2}{3}} + 2 \sqrt[3]{x + 6} \sqrt[3]{3x - 5} + 4(3x - 5)^\Big{\frac{2}{3}} \bigg] }{\Big( \sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5} \Big) \bigg[ (x + 6)^\Big{\frac{2}{3}} + 2 \sqrt[3]{x + 6} \sqrt[3]{3x - 5} + 4(3x - 5)^\Big{\frac{2}{3}} \bigg] } \\& = - \frac{1}{23} \bigg[ (x + 6)^\Big{\frac{2}{3}} + 2 \sqrt[3]{x + 6} \sqrt[3]{3x - 5} + 4(3x - 5)^\Big{\frac{2}{3}} \bigg] \\\end{aligned}\)

Substitute in the simplified function and continue:

\(\displaystyle\begin{aligned}\lim_{x \to 2} \frac{\sqrt{x + 7} - 3 \sqrt{2x - 3}}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} & = - \frac{17}{6} \lim_{x \to 2} \frac{x - 2}{\sqrt[3]{x + 6} - 2 \sqrt[3]{3x - 5}} \\& = \frac{17}{138} \lim_{x \to 2} \bigg[ (x + 6)^\Big{\frac{2}{3}} + 2 \sqrt[3]{x + 6} \sqrt[3]{3x - 5} + 4(3x - 5)^\Big{\frac{2}{3}} \bigg] \\& = \frac{17}{138} (12) \\& = \boxed{ \frac{34}{23} } \\\end{aligned}\)

∴ we have evaluated the following limit without L' Hopital's Rule.

Step 3: Geometrical Interpretation

We can also graph the given function and approximate the limit. Please refer to the attachment for visualization.

___

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Answer:

  34/23

Step-by-step explanation:

The limit can be evaluated by simplifying the expression in such a way as to cancel the offending zeros.

__

Define the following (to help keep the algebra cleaner):

  \(a=\sqrt{x+7},\ b=3\sqrt{2x-3}\\\\c=\sqrt[3]{x+6}.\ d=2\sqrt[3]{3x-5}\)

Then the desired limit is ...

  \(\displaystyle \lim_{x\to 2}\dfrac{a-b}{c-d}\)

We observe that ...

  \((a-b)(a+b)=\underline{a^2-b^2}=(x+7)-(3^2(2x-3))=-17x+34=\underline{-17(x-2)}\\\\(c-d)(c^2+cd+d^2)=\underline{c^3-d^3}=(x+6)-(2^3(3x-5))=-23x+46=\underline{-23(x-2)}\\\\\displaystyle\lim_{x\to2}{(a+b)}=3+3=6\\\\\lim_{x\to2}{(c^2+cd+d^2)}=4+4+4=12\)

In the following expression, the factors (x-2) cancel, so, our limit is ...

  \(\displaystyle\lim_{x\to2}\dfrac{a-b}{c-d}=\lim_{x\to2}\dfrac{(a^2-b^2)(c^2+cd+d^2)}{(c^3-d^3)(a+b)}=\lim_{x\to2}\dfrac{-17(x-2)(12)}{-23(x-2)(6)}=\boxed{\dfrac{34}{23}}\)

Answer:$ 24,679.20 or 514.15 a month

Step-by-step explanation: 565(.09) is 50.85 which needs to be deducted from the payment of 565 because he needs to be able to pay for interest. 514.15 is then multiplied by 48 months which will bring you to 24,679.20

The value of "x" in the given linear equation of two variable 15x - 9y = -9 will be x = 0.6(-1+y).

As per the question statement, we are given a linear equation of two variable 15x - 9y = -9  and we are supposed to solve it for the variable "x"

First step would be to isolate "x" from the given equation

15x - 9y = -9

15x = -9 + 9y

15x = 9(-1+y) [Distributive property]
x = 9(-1+y)/15

x = 3(-1+y)/5 [Simplified]

or x = 0.6(-1+y)

Hence, the value of "x" in the given linear equation of two variable 15x - 9y = -9 will be x = 0.6(-1+y).

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Rearrange unknown terms to the left side of the equation

                   \(\boldsymbol{\sf{ 9x > 50.4-9 \ \ \longmapsto \ \ \ [Subtract]}}\)

Calculate the sum or difference.

                                  \(\boldsymbol{\sf{9x > 41.4 }}\)

Convert decimal to fraction.

                                    \(\boldsymbol{\sf{9x > \dfrac{414}{10} }}\)

Reduce the greatest common factor for both sides of the inequality.

                                    \(\boldsymbol{\sf{x > \dfrac{46}{10} }}\)

Reduce the fraction

                         \(\red{ \boxed{\boldsymbol{\sf{\blue{ Answer \ \ \longmapsto \ \ x > \dfrac{23}{5} }}}}}\)

Hello!

Let's solve this inequality for x:

\(\begin{aligned} \sf{\Box\!\!\!\!\!\star{9x+9 > 50.4}\\\sf{9x > 41.4}\\\sf{x > 4.6} \end{aligned}\)

Therefore \(\bold{x > 4.6}\).

Hope that helps! :)

-art lover

Answer:

They can invite at max 112 people.

Step-by-step explanation:

4000 - 50 = 3950

3950 / 35 = 112.85 (Can't round up to 113 because then it will go over their budget), so you will get 112 people.

If the boat travel north at 30 km per hour .  the equivalent speed in still water required to achieve an actual speed of 30 km/h is 30.1 km/h.

Finding the boat's true speed using Pythagoras' theorem using this  formula

Speed = √((30 km/h)^2 + (4/√(2) km/h)^2)

Let plug in the formula

Speed = √(900 + 8) km/h

Speed = √(908) km/h

Speed = 30.1 km/h

Speed = 30 km/h ( Approximately)

Therefore  the speed is 30km/h.

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Answer:

the difference is 75.5

Step-by-step explanation:

Answer: 77.5 degrees F

Step-by-step explanation:72.8 + 2.7 = 77.5oF

Answer: 600 mm

Step-by-step explanation:

Let height of her model be x meters

So,

500x = 300

\(\begin{aligned}&\rightarrow x=\frac{300}{500} \\&\rightarrow x=\frac{3}{5}=0.6 \text { meters } \\&\rightarrow x=0.6 \times 1000 \text { millimeters } \\&\rightarrow x=600 \text { millimeters }\end{aligned}\)

Therefore, Stacy's model is 600 millimeters tall

Answer: The answer is 207.4 for the interest

Step-by-step explanation:

766.85 - 559.45= 207.4

The answer 207.4 is the amount of interest on Thayne's credit card bill.

We can find this answer by subtracting the amount of charges from the total bill amount.

Total bill amount = $766.85

Amount of charges = $1118.9

Amount of interest = $766.85 - $1118.9 = $207.4

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GIven:

The equations

Required:

Find the correct solution.

Explanation:

The equations,

And

Answer:

Answer:

61%

Step-by-step explanation:

We can see that out of all the people that were surveyed, 54% were 10th graders. Since 33% out of all the ones surveyed were 10th graders that chose robotics, the fraction would be 33/54 which is 0.611.

This is 61% approx.

Answer:

61%

Step-by-step explanation:

A P E X

Answer:

hey can you give us the buying price of the ticket so we can find the increase? thanks :)

Step-by-step explanation:

Answer:

It is rational

Step-by-step explanation:

A rational number is a number that can be written as an integer over an integer.  

Integers are all the whole numbers and their opposites.  The whole numbers are 0, 1, 2, 3, 4, etc.  There opposites would be -1 -2 -3 -4 and so on.

0.2782

can be written:

\(\frac{2782}{10000}\)

The Venn diagram for (D ⋃ E) ⋃ F will be the ovarlapped region of D,E and F.

To represent the sets D, E, and F in the Venn diagram, we first construct three overlapping circles. Then, beginning with the innermost operation and moving outward, we shade the regions corresponding to the set operations in the expression.

We shade the area where the circles for D and E overlap because the equation (D ⋃ E)  denotes the union of the sets D and E. All the elements in D, E, or both are represented by this area.

The union of (D ⋃ E) with F is the next step. This indicates that we darken the area where the circle for F crosses over into the area that we shaded earlier. All the components found in sets D, E, F, or any combination of these sets are represented in this region.

The final Venn diagram should include three overlapping circles, with (D ⋃ E) ⋃ F shaded in the area where all three circles overlap.

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angle 98 and angle 9b - 8 are supplementary angles, therefore:

98 + (9b-8) = 180

Solving for b:

98 + 9b - 8 = 180

90

Answer:

It B. Yes, because the number of tables Increase when the number of people Increase

Answer:

the answer is B . because the number of people is increasing as the number of tables is . proportional means same amount increasing :)

hopefully this helps :)

This value is approximate.

==========================================================

Explanation:

Let's compute the z score for x = 40

z = (x-mu)/sigma

z = (40-47)/7

z = -1

We're exactly one standard deviation below the mean.

Repeat these steps for x = 68

z = (x-mu)/sigma

z = (68-47)/7

z = 3

This score is exactly three standard deviations above the mean.

Now refer to the Empirical Rule chart below. We'll add up the percentages that are between z = -1 and z = 3. This consists of the two pink regions (each 34%), the right blue region (13.5%) and the right green region (2.35%). These percentages are approximate.

34+34+13.5+2.35 = 83.85

Roughly 83.85% of the one-mile roadways have between 40 and 68 potholes.